Housing rent and in Milan: evidence from a geographical discontinuity approach1

Filippo Maria D’Arcangelo IEFE – Università Bocconi

Marco Percoco PAM – Università Bocconi

September 2014

Abstract

To cope with severe problems of pollution and congestion, a road pricing scheme (the Ecopass) to enter the city centre was introduced in Milan in January 2008. This paper assesses the impact of such a policy measure on the housing market in terms of variations in rent within the treated area. To this end, we adopted a geographical difference-in-discontinuities approach, which allowed us to control for area specific factors and to identify the effect of road pricing at the boundary of the treated area. By using detailed data from 55 zones over the period 2007 to 2012, we found that the Ecopass has had a small and positive impact on housing rent, equal to +0.75%.

Keywords: road pricing, housing markets, rent, Milan, regression discontinuity

JEL Classification numbers: Q51, R21, R41, C21, C23.

1 We would like to thank Tommaso Nannicini and Barbara Chizzolini for their invaluable suggestions. Special thanks to Davide Rossi and Riccardo Fino for their help and assistance. All errors are ours and follow a random path. 1

1. Introduction

Road pricing is becoming an increasingly popular policy measure for curbing pollution and congestion in cities. The introduction of a charge for using given roads is meant to internalize external costs through an increase in transport costs and depending on the elasticity of demand, a reduction in traffic flows.

Expected outcomes of such measures are in terms of air quality, health, accidents and speed.

Variations in pollution concentration, congestion and transport costs are particularly important in an urban context, because of their impact on individual well-being and ultimately, on housing prices

(Eliasson, 2009).2

Milan, along with London, Stockholm and Singapore, is one of the few metropolitan cities that have implemented an urban road charging scheme. In January 2008, the “Ecopass” was launched in order to reduce pollution through a reduction in the number of highly polluting vehicles in circulation.

The Ecopass programme was applied within a designated restricted traffic zone corresponding to the central “Cerchia dei Bastioni” area of 8.2 km.2 The amount of the charge depended on the vehicle’s engine emissions standard and fees varied from €2 to €10, from 7:30 to 19:30 on weekdays. Free access to the zone was granted to motorbikes, to several types of alternative fuel vehicles and to conventional fuel vehicles compliant with the European emission standards Euro 3 and Euro 4 or better.

Several papers have already analysed the effect of road pricing in Milan. Rotaris et al. (2010) proposed a cost-benefit analysis in which the Ecopass passed the test by about €6 million per year.

2 For a review of works relating housing prices and environmental amenities, Colwell and Dilmore (1999). 2

However, the analysis was carried out using descriptive statistics on pollution concentration, in which the identification of the policy effect was particularly weak. To deal with this issue, Percoco (2013) proposed the use of a regression discontinuity design and found that the charge significantly decreased the concentration of some pollutants (especially carbon monoxide and ), but only in the short run, as one week after its implementation, pollution had returned to its pre-treatment levels. By using a regression discontinuity design and a synthetic control method, Percoco (2014a;

2014b) found that the charge increased the usage of motorbikes, hence potentially worsening environmental conditions in the city.

Whether the Ecopass has had an impact on housing prices in Milan has long been and remains a popular topic in public debates and in newspapers.3 In 2009, the urban government commissioned a study to evaluate the impact of the charge on the housing market. Pragma (2009) aimed at investigating the effect of the pollution charge on the housing market a year after the introduction of the Ecopass by interviewing real estate agents. The survey led to the conclusion that a small or null effect was expected on house prices and that the sign of the effect was uncertain. While being somewhat informative at the time, the analysis was based on the personal opinions of real estate agents who may have been biased or not necessarily aware of all the details of the Ecopass.

From a theoretical perspective, the impact of road pricing on housing rent is not clear a priori, since two opposite forces may be operating in this context. The reduction in external costs in terms of pollution and congestion may in fact increase rent. On the other hand, an increase in transport costs induced by a second-best tax may reduce the willingness of individuals to pay and hence, rent will decrease. Consequently, it is an empirical matter whether the former or the latter force prevails.

3 See for example Mancini (2008) and Viarengo (2012). 3

In this paper, we assessed the causal impact of the Ecopass on housing rent. To this end, we adopted a geographical difference-in-discontinuities approach, i.e., a regression discontinuity design with two running variables (time and space), which allowed to account for area-specific unobserved variables.

Our method relaxed the strong smoothness in the covariates assumption of a classic regression discontinuity approach, as well as the common trend assumption of difference-in-differences models.

Our method therefore identified the short run impact of the policy at the boundary of the treated area.

By using data pertaining to 55 areas in Milan over the period 2007 to 2012 with a bi-annual frequency, we found that the Ecopass has increased housing rent by 0.75% and that this effect was robust across several specifications.

Percoco (2014c) recently estimated the impact of Ecopass on housing prices by using a difference- in-differences model and finding a negative effect of the policy. The research presented in the present paper differs from Percoco (2014c) in two important ways. First, we made use of housing rent instead of prices, as we believe that housing prices revealed by market transactions adjust slowly to structural policies, whereas the rental market is less small and hence, rent may react promptly to an event such as the introduction of the Ecopass. Second, we made use of a geographical difference-in- discontinuities model that allowed us to obtain precise estimates of the effect at the boundary of the treated area. The assumptions needed for this identification were more realistic than those needed for the identification of policy parameters in a difference-in-differences model.

The paper is organized as follows. Section 2 presents a description of the structure of the Ecopass.

Sections 3 and 4 present the applied methodology and data, respectively, whilst results of the econometric analysis are provided in section 5. Section 6 concludes the study.

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2. Road pricing in Milan

Milan is Lombardy’s primary city and with 1.3 million inhabitants, is the second most populated city in . Its metropolitan area extends broadly around the inner city and is estimated to host some 5.2 million people. More than 2.3 million vehicles move within and into the inner urban area every day, half of them arriving from outside the urban area (AMMA, 2008; AMAT, 2012a).

Public transportation is mainly provided by Azienda Trasporti Milanesi (ATM), the society of public transportation systems, which serves Milan and 56 adjacent municipalities through a network of four underground lines, 19 tram lines, 98 bus lines, and three trolley bus lines (AMMA, 2009, 2010).

The city was (and still is) characterized by a high motorization rate compared to other European cities; in 2007, there were 558 cars per thousand inhabitants in Milan (Percoco, 2010). The reliance of city users on cars was a major cause of the severe affecting Milan, prompting a concentration of particulates systematically above that of European standards.

Building on the experiences of other cities, a pollution charge (the so-called Ecopass) was first introduced in January 2008. In January 2012, the Ecopass was substituted by a different scheme, called Area C, in the form of a pollution charge, following a radical improvement in the emission factors of circulating vehicles due to car renovations induced by the Ecopass. The Ecopass’ rationale drew upon the “polluter-pays principle”, contained in Directive 2004/35/CE, which focused on providing different charges for different emission vehicle classes (“Euro” classes).

A toll area of 8.2 km2, roughly identified by a major circular road that encircles the city centre, the so-called “Cerchia dei Bastioni”, was identified and monitored using 43 cameras recording car number plates. The area defined by Ecopass' cordon comprised 4.5% of the municipality's breadth and 6% of its population (77 000 inhabitants).

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The road pricing scheme was effective from 7.30 to 19.30 during working days and was applied to all vehicles that crossed one of the gates equipped with cameras. By paying the charge, the vehicle obtained full access to the area for the entire day. Vehicles were divided into five categories based on their PM10 emission factors (COPERT IV model). The first two categories (alternative fuel vehicles and new Euro class vehicles) were exempted, while vehicles in the other three categories had to pay a charge, respectively, of €2, €5 and €10. Residents inside the area had the opportunity to subscribe to yearly passes at a price equivalent to 10% of full year access.

At the outset, about 50% of circulating vehicles was potentially subject to the tariff, but the gradual substitution of older and highly polluting vehicles with new cleaner ones progressively reduced this number.

The strong consensus among Milan’s population about the usefulness of the charge,confirmed by a referendum in June 2011 and the declining impact of the former road charge gave rise to a new road pricing scheme. “Area C” has been operative since 16 January 2012 and has the same geographical scope as the Ecopass. The system foresees three different access regimes for vehicles according to their motorization: total prohibition, standard access regime and exemption from the payment. A partial exemption is provided to residents inside “Cerchia dei Bastioni” – they have 40 non- consecutive free access days each year. After that, entrance costs them €2/day instead of €3. As a concession to retailers, a discount was introduced in 2013 in favour of freight vehicles and vehicles destined for private parking lots in the area. Categories of exempted vehicles also expanded up to

48% – 12% clean vehicles, 29% authorized vehicles, 7% service vehicles, while 12% were resident vehicles.

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Concerning the effects of road pricing, AMAT (2012b) reported that the number of vehicles decreased, with respect to the pre-Ecopass period, by 14.6% in 2008 (the year of the introduction of the pollution charge), 15.7% in 2009 and by 12.9% in 2010. In 2011, traffic in the area unexpectedly continued to decrease (-20.0%) due to an economic crisis effect reducing the use of cars. Nevertheless, a progressive shift toward non-paying classes of vehicles raised awareness about the sustainability of the measure. In fact, the share of charged vehicles to exempted vehicles fell from 0.23 in 2008 and

2009 to 0.15 in 2010; in 2011, as few as 14% of accessing vehicles paid the charge (11 431 vehicles out of 80 799).4 AMAT (2012c) also attempted to isolate in its studies the effect of the policy by studying the area outside the charged zone. The results (in terms of difference in congestion reduction) were estimated to be a reduction ascribable to the Ecopass of 10.7% in 2008, 8% in 2009 and 6% in 2010. AMAT (2012c) further reported that in 2012, the number of entrances in the congestion charge area had diminished from 131.898/day in 2012 to 90.849/day in 2011 (-31.1%).

3. Methodology

In order to estimate the treatment effect of the policy, we used a geographic regression discontinuity design (RDD), controlling for dynamic differences over a geographic forcing variable. This approach allowed us to overcome some of the limitations of simple discontinuity design by isolating the possible confounding effect of intrinsic differences among areas. The RDD design was introduced by

Thistlewaite and Campbell (1960) and has been widely used in the study of impact evaluation since then5 when dealing with the fundamental problem of causal inference, i.e., the impossibility to observe, for the same unit, outcomes under treatment and non-treatment status (Rubin, 1974; Holland,

1986).

4 Our calculations on AMAT (2012b; 2012c) data. 5 For recent overviews see Imbens and Lemieux (2008) and Lee and Lemieux (2010). 7

RDD isolates the local treatment effect by setting up a quasi-experiment in which assignment to treatment and control group is made by the “assignment variable”. In our case, the assignment variable was the minimum distance of each zone from Milan’s centre. The cut-off point (the point where the policy, i.e., the Ecopass starts) was at 1.13 kilometres from the Duomo (and the centroid of the area), which we assumed to be the central point. Each zone not included in the Ecopass area was outside this range and each zone included in the Ecopass area was within it. The probability of assignment to the policy was either zero or one and was completely deterministic, i.e., this RDD setting is “sharp”.

Consider the following model:

푌 = 훼 + 휏퐷 + 훿(퐶∗) + 휀 (1) where 푌 is the logarithmic transformation of the monthly rent; 훿(∙) is a polynomial function of order 푔; 퐶∗ is the distance normalized to be zero at the cut-off (푐 = 1.13 km); 퐷 is the treatment variable, which captures if the zone is within the treated area:

1 푖푓 퐶∗ ≤ 0 퐷 = { (2) 0 푖푓 퐶∗ > 0

The local treatment effect, 휏푅퐷퐷, was defined as:

휏 = lim Ε[푌|퐶∗ = 휀] − lim Ε[푌|퐶∗ = 휀] 휀↑0 휀↓0 (3)

An accepted identification assumption that underlies RDD is that the conditional distribution function is smooth in the covariates, i.e., that differential benefits from assignment are the only source of discontinuity in outcomes concerning the cut-off (Hahn et al., 2001). Lee and Lemieux (2010) argue that, given such an assumption, it is irrelevant to include baseline covariates in order to obtain RDD consistent estimates. This is due to the approximation given by the polynomial of order 푔, which smoothens the regression and becomes arbitrarily accurate as 푔 → ∞. However, the treatment effect estimated cannot be interpreted as the total effect on treated, but merely as a local treatment effect.

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This in turn means that the estimation of policy effects is more accurate in a narrow interval around the cut-off.

The model in (1) correctly predicted the effect of being inside Cerchia dei Bastioni. However, it was confounded by a discontinuity at the cut-off and is therefore biased. The identification assumption, in fact, imposes that all the factors that influence prices must evolve smoothly with respect to the assignment variable. In our case, however, we faced a sampling bias inherent to the nature of housing in Milan. Buildings that are close to the city centre are per se more expensive, as they are generally in better condition or have better standing. In other words, being inside the treatment area (which indeed influenced the dependent variable) is a feature that did not change continuously along the assignment variable. In a single treatment year, the RDD estimator presented in (3) was therefore confounded as it also measured the effect of being inside the city centre.

To deal with this problem, we made use of rent payments observed over time as an outcome variable.

While amenity conditions did not vary smoothly in the assignment variable, they were nevertheless comparable over time. In fact, no significant change affected the contextual conditions of the housing market inside and outside the road pricing area.

Let us consider the following assumptions (Grembi et al., 2011):

∗ Assumption 1: Ε[푌푖푡(0)|퐶푖, 푇 = 1] − Ε[푌푖푡(0)| 퐶푖, 푇 = 0] is continuous in 퐶

∗ Assumption 2: Ε[푌푖푡(1) − 푌푖푡(0)| 퐶푖, 푇 = 1] is continuous in 퐶

Assumption 1 is a “smoothness” condition, as it requires that the temporal difference of prices in the case of no policy is not asymmetrically affected over time by unobservables around the cut-off. In other words, covariates (Ci) that explain the temporal difference, should not “jump” at the cut-off, but have identical distributions on either side of it. Assumption 1 is the same as assuming a time-invariant difference in rent payments due to the market, which seemed reasonable in our setting, although

9 untestable. If Assumption 1 held, average treatment on treated (퐸[푌푖(1) − 푌푖(0)|퐷 = 1]) could be calculated.6

Assumption 2 required the average treatment effect to be explained only by the discontinuity. In other words, prices inside and outside the area must react similarly to road charging. Again, help in satisfying the assumption came from the log transformation, which imposes comparing percentage changes instead of the level of rent payments.

To sum up, we imposed that the market influenced buildings close to the treated area similarly and that road charging was able to exert similar effects on similar buildings. Assumption 2 was violated if buildings directly inside the treated area had an intrinsic advantage (or disadvantage), which was reflected in the level of rent, compared to those right outside the treated area.7 If Assumptions 1 and

2 held, a local average treatment effect (퐸[푌푖(1) − 푌푖(0)]) could be calculated.

Keele and Titiunik (2013) establish further identifying assumptions in geographic regression discontinuity design by proving that geographical RDD is a particular case of a RDD with two running variable. However, our case was what is referred to as “naïve distance”, as our running variable was a simple distance from a given boundary. When using such a design, no further assumptions are required.

Under Assumptions 1 and 2, the estimator identified a local causal effect for time 푡, 휏, defined as follows:

6 Recall that 푌(1) is the outcome under treatment, 푌(0) is the outcome with no treatment and 퐷 휖[0,1] is the treatment variable. 7 This assumption appears somehow like the usual “common trend” assumption of diff-in-diff. It is in fact very different: the common trend is assumed only at the discontinuity, rather than on average values, for both the treatment and the control group. 10

푇=1 푇=0 휏 = [lim Ε[푌|퐶∗ = 휀] − lim Ε[푌|퐶∗ = 휀]] − [lim Ε[푌|퐶∗ = 휀] − lim Ε[푌|퐶∗ = 휀]] (5) 휀↑0 휀↓0 휀↑0 휀↓0

Figure 1 clarifies how the (local) average treatment effect is calculated, as it shows a simple bid-rent function in a monocentric city (as in the case of Milan). In period 푇 = 0, the policy was not active and we are able to observe only the difference between untreated subjects at the cut-off (B). The difference between the two groups in case of treatment (A) was not observable. In period 푇 = 1, the

Ecopass was implemented; thus, we were able to observe its effect on the treated area at the left of the cut-off in comparison with those at the right, outside the Cerchia dei Bastioni. The differences (E) were also observable. We were unable to observe what would have happened to the treated area in case the differences were unobservable; however, if Assumption 1 held, then 퐵 = 퐷 and therefore the average treatment on treated (ATT) would have been 휏 = (퐸 − 퐷) = (퐸 − 퐵). If Assumption 2 held, then A=B and the counterfactual effect would have been average treatment effect (ATE).

[Figure 1]

We investigated the dynamic RDD causal effect using the following random-effects estimation:

∗ 푌푖푡 = 훼 + 훾퐷푖 + 휔푇푡 + 휏퐷푖푇푡 + 훿(퐶푖 ) + 훽(푋푖푡) + 푢푖푡 (6) where 푇푡 is a time dummy, assuming a value of 1 when the Ecopass was introduced (i.e., after January

2008); 푋푖푡 is a set of covariates included to address possible geographic or temporal differences across buildings; 푢푖푡 is the random-effect error; other variables are those of (1). Among the variables in vector X, we included a temporal trend, a dummy indicating the semester of the year to account for possible cyclicality, dummies for the types and for the status of preservation, as well as a series of interactions between these dummies and the treatment status. It should be noted that, in a RDD framework, the running variable in its polynomial transformation is by its construction enough to identify the policy parameter in terms of orthogonality between the running variable (in our case,

11 distance from the city centre) and all other covariates assumed. However, to relax this assumption, we also estimated a set of regressions in which the aforementioned control variables were used.

The inclusion of several interaction terms was particularly important in our case, as data for the concentration of pollutants for the 55 areas were not available. However, despite the orthogonality assumption, we believe that this exclusion is not a source of main concern, because our particular geographical RDD model identified the policy parameter at the border of the treated area. Ideally, the

ATT is estimated by comparing an average treated zone on the border with its neighbouring control zone. As pollution did not exhibit discrete jumps across space, one can reasonably assume that pollution concentration was continuous across the border and as such, it is orthogonal to the policy variable and hence did not affect estimates of the ATT.

4. Data

To estimate model (6), we made use of data pertaining to housing rent from the Agenzia delle

Territorio, which is the Italian cadastral agency. These data were collected from market transactions by the agency itself and were aggregated according to zones of homogeneous buildings.8 Our dataset was structured as a panel of six years, from 2007 to 2012, each divided into half-year periods (twelve periods in total). Rent payments were corrected as per the consumer price index provided by ISTAT

(Italian National Institute of Statistics) in order to obtain real rental payments at 2012 prices. Despite data having been aggregated according to homogeneous buildings and urban areas, they encompassed different preservation statuses: normal, poor quality and high quality. We focused our analysis on residential buildings belonging to two typologies: lower-tier (economic flats) and upper-tier buildings

(terraced houses, high-end flats, lofts). We excluded villas and peculiar residential buildings. As the data had been, we did not have precise information on houses’ individual characteristics; however,

8 Peculiar buildings and outliers are excluded by Agenzia del Territorio from the survey. 12 the classifications provided by Agenzia del Territorio controlled to a certain extent for the comparable conditions of buildings.

[Figure 2]

Milan is divided by the agency into 55 zones: 10 central, 12 semi-central, 29 peripheral and four suburban (Figure 2). The 10 central zones lie inside Cerchia dei Bastioni, i.e., the area affected by the

Ecopass, with the relevant exception of “zone B02” in the north, which is partially outside the area.

We decided to consider this zone as fully treated, being that it is inside the road pricing area for the most part.9

For each semester, we had 330 observations: one for each preservation status and for both lower- and upper-tier type of buildings in each zone. Tables 1 and 2 report the descriptive statistics of our sample across zones and typologies of buildings.

[Figure 3; Tables 1 and 2]

Figure 3 shows how rent is distributed over the distance from the centre: the further the houses were from the centre, the less their average rent. This relation was quite strong and robust enough to considering averages over the period of observation. A discontinuity was evident around the cut-off point (1.13 km): houses inside Cerchia dei Bastioni were more expensive than those outside the cut- off point. This jump had already been evident prior to the Ecopass being introduced, meaning that there was an intrinsic difference between the two areas. Thus, a usual RDD, performed after the

9 Econometric results are not affected by this choice. 13 introduction of a road charge, would not have identifies a credible counterfactual. This descriptive evidence corroborates our decision of applying a geographical difference-in-discontinuities model.

[Figure 4]

In Figure 4 we have replicated a similar scatter plot as in Figure 3; however, in the former, we aimed to observe (only from a descriptive point of view) the behaviour of the growth of housing rental payments around the cut-off. A clear vertical discontinuity did not emerge, indicating a null effect of the Ecopass. However, this descriptive evidence needs to be corroborated by an econometric analysis that takes into account the variety of types of houses in our sample, as well as different forms of the trend in the running variable.

5. Results

Equation (6) was estimated on the log transformation of (real) rental payments for 푔 ∈ [1, 2, 3, 4], i.e., including a polynomial of the running variable up to the fourth order.

Table 3 reports the results of the RDD regressions with random effects. Additional covariates have been progressively introduced to test the assumption of (dynamic) smoothness in the covariates. None of the introduced covariates affected the final results, thus reinforcing the assumption of orthogonality with respect to the treatment variable. It is worth noting that belonging to the treatment group, i.e., being inside Cerchia dei Bastioni, implied higher rent: around 60% more on average. Overall, the market has been contracting in real terms since 2007 and the “trend” variable showed a reduction of

1.2% each semester on average. Other variables, such as the preservation status and house typologies, had the expected sign.

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Further to be noted is that, across models (1) − (3) in Table 3, we have progressively introduced several interactions to control for possible time-invariant heterogeneity arising across typologies of buildings and preservation status.

In order to investigate the effect of the Ecopass, our variable of interest was Policy, i.e., the interaction between Treatment (being inside the area) and Time (equalling one after the introduction of the

Ecopass). The average effect of the policy was statistically significant at 99% in all regressions. The coefficient, equal to 0.75%, was robust across models, suggesting strong independence from other possible factors included in the estimates.

In Table 4, we have introduced several higher order polynomials of the geographical distance to check whether non-linear spatial trends may have altered results with respect to the linear result. Results in this case also remained extremely robust, even in terms of standard errors.

A possible shortcoming of our geographical RDD approach was that it included distant and therefore incomparable buildings. In order to reduce the risk of overestimating the policy effect, we conducted a robustness check, including a narrower area as counterfactual, i.e., we restricted the control group.

We compared our treatment area (the one inside Cerchia dei Bastioni) only to the semi-central zone, thus excluding peripheral and suburban zones and as such, reduced the maximum distance from the centre to 4.27 km (rather than 10.18 km). Results in model (1) in Table 5 remained noticeably unchanged, with a slight decrease in the policy coefficient from 0.75% to 0.71% and therefore showing similar statistical significance.

[Tables 3, 4, 5]

Finally, model (2) in Table 5 reports OLS estimates of (6) with pooled standard errors for comparison. In this case, the policy coefficient also remained equal to 0.75%. 15

As stated in the introduction, Percoco (2014c) already studied the effect of the Ecopass on housing markets and found a decrease in market prices by 1.2 to 1.8% in the treated area. In efficient markets, housing prices equal the discounted flow of future rent payments, therefore prices and rent should be positively correlated. Under this strong efficiency condition, the results presented in this paper are therefore the opposite of estimates found by Percoco (2014c). There may be several reasons for this outcome. First, the efficiency assumption of housing markets may not hold in reality, so that prices may not perfectly reflect the flow of future rent payments. Second, both Percoco (2014c) and the research in the current paper estimated the reaction of housing markets to the introduction of road pricing in the short run. This implies that the adjustment pattern of prices may differ from that of rent.

We believe that rental payments are less sticky than house prices and are likely more reactive to policy innovations. Third, Percoco (2014c) made use of a simple difference-in-differences model with several robustness checks. Our geographical difference-in-discontinuities approach provided more robust estimates of the policy impact, due to less restrictive assumptions. Therefore, the estimated model in Percoco (2014c) may have been miss-specified.

6. Conclusions

In this paper, we investigated the effect of Milan’s road pricing in the form of the Ecopass on the housing market in terms of rental payments. We made use of a geographical regression discontinuity estimator in a dynamic quasi-experimental setting, which provided a solid counterfactual for isolating the contribution of the policy.

We found the benefit of a perceived reduction of negative externalities to be well-received by inhabitants, who have been willing to pay 0.75% more for such an improvement. This result was significant to different specifications and robustness checks. In practice, such an increase has implied 16 higher rental rates on average: a typical 100m2 apartment has seen its yearly rent increasing by roughly €175. Such an increase exceeds the Ecopass’ annual costs for residents in the treated area in all cases, with the exception “class 5” vehicles.

We believe that further research might focus on microdata in order to estimate more specifically a hedonic price model that will refine the estimation of the impact of road pricing on housing markets.

References

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Lee, D. S. and Lemieux, T. (2010). Regression Discontinuity Designs in Economics. Journal of Economic Literature 48, 281-335.

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Figure 1: Dynamic RDD estimation strategy.

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Figure 2: Housing market zones in Milan

Figure 3: Distribution of rents over distance from centre

4

3

log rents log

2

1

-2 0 2 4 6 distance

logloc_medr 95% CI Fitted values Fitted values

Notes: Rents are log-transformations of OMI zone averages at 2012 constant prices. Distance is calculated as the geographical distance (in km) of the closest point of the homogeneous OMI zone. Two quadratic curves fit values before and after the discontinuity (1.13km). Confidence intervals at 95% in the shaded area. 20

Figure 4: Average growth in rents across space (2007-2012)

Notes: Two quadratic curves fit values before and after the first year. Confidence intervals at 95% in the shaded area.

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Table 1: Descriptive statistics across zones

Standard Zone N Mean Deviation Central 720 19.42 6.15 Semi-central 864 10.19 2.96 Peripheral 2,088 7.45 2.30 Suburban 288 7.05 2.00 Whole city 3,960 10.19 5.66

Table 2: Descriptive statistics across typologies

Preservation status

poor normal high total lower-tier mean 8.88 10.70 14.46 11.35

s.d. 4.42 5.13 6.64 5.95 upper-tier mean 7.31 8.80 11.02 9.04

s.d. 4.16 4.57 5.76 5.11 Total mean 8.10 9.75 12.74 10.19

s.d. 4.36 4.95 6.45 5.66

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Table 3: Dynamic linear RDD estimation Average (log) rents at constant prices (1) (2) (3)

NDistance -0.0907*** -0.0907*** -0.0907*** (0.0132) (0.00863) (0.00861) Treatment [D(i)] 0.628*** 0.628*** 0.598*** (0.0556) (0.0364) (0.0718) Time [T(i)] -0.00613*** -0.00613*** -0.00587*** (0.00124) (0.00124) (0.00124) Policy [T(i) × D(i)] 0.00749*** 0.00749*** 0.00749*** (0.00230) (0.00230) (0.00230) trend -0.0120*** -0.0120*** -0.0120*** (0.000125) (0.000125) (0.000128) 2nd semester 0.00122* (0.000672) Poor preservation [Baseline]

Normal preservation 0.202*** (0.0409) High preservation 0.512*** (0.0409) Upper-tier type [Baseline]

Lower-tier type -0.242*** (0.0409) Types × preservation Yes Yes

Treatment × preservation Yes

Treatment ×types Yes

Treatment × preservation × type Yes

Constant 2.329*** 2.219*** 2.224*** (0.0347) (0.0330) (0.0348)

Observations 3,960 3,960 3,960 Number of id 330 330 330 Notes: Random effects estimation. Standard errors in parentheses. Significance: *** p<0.01, ** p<0.05, * p<0.1. Full interaction outputs have been omitted for the sake of clarity, but are available on request.

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Table 4: Dynamic RDD estimator with different orders of polynomial Average (log) rents at constant prices Order of polynomial 1° 2° 3° 4°

NDistance -0.0907*** -0.227*** -0.307*** -0.313*** (0.00861) (0.0258) (0.0368) (0.0372) NDistance^2 0.0282*** 0.0771*** 0.0567** (0.00505) (0.0170) (0.0255) NDistance^3 -0.00714*** 0.00395 (0.00238) (0.0106) NDistance^4 -0.00140 (0.00130) Trend -0.0120*** -0.0120*** -0.0120*** -0.0120*** (0.000128) (0.000128) (0.000128) (0.000128) Time [T(i)] -0.00587*** -0.00587*** -0.00587*** -0.00587*** (0.00124) (0.00124) (0.00124) (0.00124) Policy [T(i) × D(i)] 0.00749*** 0.00749*** 0.00749*** 0.00749*** (0.00230) (0.00230) (0.00230) (0.00230) Treatment [D(i)] 0.598*** 0.410*** 0.334*** 0.327*** (0.0718) (0.0764) (0.0796) (0.0799) 2nd semester 0.00122* 0.00122* 0.00122* 0.00122* (0.000672) (0.000672) (0.000672) (0.000672) Normal preservation 0.202*** 0.202*** 0.202*** 0.202*** (0.0409) (0.0391) (0.0386) (0.0386) High preservation 0.512*** 0.512*** 0.512*** 0.512*** (0.0409) (0.0391) (0.0386) (0.0386) Lower-tier type -0.242*** -0.242*** -0.242*** -0.242*** (0.0409) (0.0391) (0.0386) (0.0386) Types × preservation Yes Yes Yes Yes

Treatment × preservation Yes Yes Yes Yes

Treatment ×types Yes Yes Yes Yes

Treatment × preservation × type Yes Yes Yes Yes

Constant 2.224*** 2.336*** 2.354*** 2.369*** (0.0348) (0.0388) (0.0388) (0.0414)

Observations 3,960 3,960 3,960 3,960 R-squared 0.832 0.847 0.851 0.852 Number of id 330 330 330 330 Notes: Random effects estimation. R-squared presented is overall. Standard errors in parentheses. Significance: *** p<0.01, ** p<0.05, * p<0.1. Full interaction outputs have been omitted for the sake of clarity, but are available on request.

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Table 5: Robustness check and OLS comparison Average (log) rents (1) (2) at constant prices Robustness Pooled OLS check

NDistance -0.164*** -0.0907*** (0.0426) (0.00686) Treatment [D(i)] 0.424*** 0.598*** (0.0926) (0.0736) Time [T(i)] -0.0126*** -0.00587*** (0.00273) (0.00139) Policy [T(i) × D(i)] 0.00716** 0.00749** (0.00341) (0.00355) Trend -0.0109*** -0.0120*** (0.000245) (0.000225) 2nd semester 0.00200 0.00122*** (0.00129) (0.000342) Poor preservation [Baseline] [Baseline]

Normal preservation 0.196*** 0.202*** (0.0738) (0.0383) High preservation 0.507*** 0.512*** (0.0738) (0.0368) Upper-tier type [Baseline] [Baseline]

Lower-tier type -0.242*** -0.242*** (0.0738) (0.0396) Types × preservation Yes Yes Treatment × Yes Yes preservation Treatment ×types Yes Yes Treatment × Yes Yes preservation × type Constant 2.361*** 2.224*** (0.0604) (0.0337)

Observations 1,584 3,960 R-squared 0.836 0.832 Number of id 132 330 1Notes: Random effects estimation (1) and OLS with pooled standard errors (2). R-squared for r.e. regression is overall for re estimation. Standard errors in parentheses. Significance: *** p<0.01, ** p<0.05, * p<0.1. Full interaction outputs have been omitted for the sake of clarity, but are available on request.

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