The importance of crime severity for housing prices

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The importance of crime

severity for housing prices

- Implementation of criminal harm weighting into the

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Acknowledgments

The author would especially like to thank associate professor Joakim Jansson for his role as a supervisor throughout this thesis.

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Abstract

The empirical results from past research are quite clear. When the

surrounding crime level goes up, housing prices go down. However, what has not been acknowledged in the previous literature is that different crimes might impact our willingness-to-pay heterogeneously. As most of the

previous research is done through the usage of simple crime rates, this thesis acknowledges the relative severeness of different crimes. Using the newly developed crime harm index (CHI), the relative severity and harm inflicted by a specific crime is identified. The study is conducted in Sweden,

Stockholm, using data for the year 2020. With the use of hedonic price equations, spatial models as well as graphical information system software, this thesis estimates a significant, and non-negligible negative relationship between increased area mean CHI and apartment prices. To the best of the author’s knowledge, this is one of the very first analyses within the literature, which acknowledges the relative severeness of crimes, and the first to show a significant negative relationship between increased criminal harm and

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1. Introduction

What impact might surrounding crime levels have on our willingness-to-pay for housing? How much are we willing to pay to move further away from crime? The impact of criminal activity on housing prices is an area of research that is quite well researched outside of Europe, especially in the United States. In the late 70s, Thaler (1978) was one of the very first to publish empirical evidence that crime may reduce housing prices by up to approximately 3 percent. Similar negative relations between housing prices and an increase in neighboring crimes are expected to be empirically found still today.

What has not been researched to the same extent is how different crimes might impact prices heterogeneously. Different types of crime might very well have a different impact on our perceived security and willingness-to-pay for housing. To neglect the relative severeness of different crimes as the majority of previous papers has done, should hence not be plausible. Cohen (1990) argued that estimating the willingness-to-pay for reduced crime by only using a simple measure of the number of crimes reported, implies that we put the same “value” on all types of crimes. Cohen (1990) meant that weighting crimes by seriousness could make areas with similar crime rates differ substantially in public safety.

This thesis will move the analysis to Sweden, Stockholm, and expand on Cohen’s (1990) early suggestions by implementing crime severeness weighting into the literature. It will do so using the recently developed, and arguably objectively constructed, Crime Harm Index (CHI), in a search for answers to the research question:

Will using the newly developed Crime Harm Index (CHI), which

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housing prices differently to previous Swedish studies simply using crime rates and hot-spots?

With the help of this new and alternative CHI measure, this thesis shed light on a new, and potentially a more insightful way of estimating the actual cost of crimes on housing prices, compared to previous literature that simply uses crime rates. A way in which the relative harm of different crimes is

acknowledged.

Through the use of sophisticated spatial models to account for the spatial dependence in the data, this thesis estimates a significant and non-negligible negative relationship between apartment prices and an increase in the relative severity of the neighboring crimes. The results are what seems, a first of its kind.

To the best of my knowledge, even though Cohen’s (1990) early suggestions, only one previous study has actually tried to implement some weighting of the seriousness of the crimes, when looking at the effect of crime on the housing market. Back in the year 2001, Lynch and Rasmussen (2001) used a monetary cost estimate of specific crimes developed by Cohen et al. (1995). The analysis was performed on Jackson, Florida, and their findings suggested no significant relationship between the cost of crime and the housing prices. However, this approach taken from Cohen et al. (1995) used in Lynch and Rasmussen (2001) has been greatly criticized, for example by Butterfield (1996) regarding their ways of measuring physical costs. Trying to assign a monetary cost to a crime is highly complex. Ashby (2018) argues that

quantifying harm inflicted by a crime monetarily, is highly subjective and the final cost can consist of financial costs, injuries, mental harm, social harm as well as the destruction of the environment.

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decisions, urban planners and insurance companies to mention a few

examples. Research on the area can also further help to estimate the societal costs of crime. Precise cost estimates of criminal activity are key for actors to perform good decision-making on safety investments et cetera.

However, the relationship between crime and the housing market is evidently, as will be discovered throughout this thesis, not an easy area to conduct empirical research on. The housing market, like most markets, is very complex. The buying decision is influenced by a large number of factors, some more common and some more specific to each individual. Being able to perform good statistical analysis and argue for complete control of possible external influencers to housing prices, are therefore extremely demanding.

Controlling for the surrounding areas different attributes, expected to be either negatively or positively affecting housing prices, helps to reduce endogeneity. Hence, this thesis will include controls for the nearest neighborhood features such as distance to the waterfront, schools, public transports, and highways, all mentioned by previous literature to have an important implication on housing prices.

Further, the CHI measure used in this thesis may, additionally to better reflect the relative harm inflicted by a specific crime, also make the results of the analysis less prone to experience reverse causality. Ceccato and

Wilhelmsson (2011) argue that some crime types such as burglaries run the risk of experience reverse causality towards housing prices. The CHI

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The remainder of this article is organized as follows. Section 1 will consist of a literature review of past relevant literature. Section 2 thoroughly introduces the Crime Harm Index to the reader and prepares it to be utilized in the settings of this thesis. Section 3 presents the data as well as the

methodological approach. Section 4 presents the estimation results and section 5 consists of final considerations.

2. Literature review

In summary and throughout time, researchers in the literature have been using many different types of crime measures to empirically estimate the effect on housing prices. Some have used the rate of assaults and robberies (Weisbrod et al., 1980), some have used the rate of property crimes (Burnell, 1988) as well as simply total crime rates (Naroff, Hellman and Skinner, 1980); (Case and Mayer, 1996). Even the location of sex offenders is used as a factor in some studies (Linden and Rockoff, 2008); (J. C. Pope, 2008); (Caudill, Affuso and Yang, 2015). Some researchers have looked at the effect from simply the fear of criminal activity (J. C. Pope, 2008). Further, densities of total crimes are also used (Ihlanfeldt and Mayock, 2010); (Bowes and Ihlanfeldt, 2001).

Close to all of the past literature, irrespectively of criminal measure chosen, have shown similar negative effects on housing prices as Thaler (1978) did already back in the late ‘70s.

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Within Sweden, Ceccato and Wilhelmsson are together the clear dominant provider of empirical research regarding the relationship between crime and housing prices.

Similar to past researchers outside of Sweden, Ceccato and Wilhelmsson have mainly looked at the impact on housing prices using the absolute rate of crime. They have done so in slightly different ways, including some standard approaches such as the ordinary least squares and the use of instrumental variables. Additionally, more spatially oriented models have also been applied, such as the spatial lag model as well as the spatial error model (see section 4.2. for further discussion). These spatial models are developed to take into account the spatial dependence that spatial data tend to experience. (Ceccato and Wilhelmsson, 2011); (Wilhelmsson and Ceccato, 2015); (Ceccato and Wilhelmsson, 2018).

Ceccato and Wilhelmsson (2012) extended from using only rates of different crimes, adding the experienced fear of exposure to crime as a factor.

Common for all their findings is that increased crime, independent of whether measured in rates or fear, is related to lower housing prices. Simply the fear of crime was interestingly found to be significantly negatively relating to housing prices, even when crime rates were controlled for. In their most recent work, Ceccato and Wilhelmsson (2020), they introduce the concept of crime hot-spots. Instead of only assessing the effect on

housing prices from the rate of crimes, they also assessed the effect on prices from being close to a crime hot-spot. Doing so, they effectively counter-acts the potential issue of having to assume a uniform risk of crime. Their

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house one kilometer further away from a crime hot-spot would increase its value by more than 30 000 SEK.

Common for their studies is the use of Geographical information systems (GIS) and spatial analyses, making them able to incorporate information such as neighborhood characteristics and conditions. This is a crucial and vital tool in being able to counteract the concerns of endogeneity. As Gibbons (2004) concluded, crime rates will be endogenous to housing prices if not all attributes are observed. Some of these attributes are the different

neighborhood characteristics and through the use of GIS software, these attributes are possible to observe and control for.

This thesis will extend on the solid work already done in the field of crime and housing prices within the Swedish borders, and further provide an alternative way of estimating the actual cost of crime on housing prices, acknowledging the relative harm of each crime.

3. The Crime Harm Index

3.1 Background

For a long time, criminal activity has been measured at pure rates. In a statistical sense, this means that two completely different crime types have still received equal weighting in the records. It is not wrong per se to say that total crime has decreased if it during period t+1, compared to period t has been three fewer shopliftings, but only two more physical assaults. However, it would not be rational nor plausible to suggest that the actual total harm inflicted from the criminal activities in period t+1 has decreased compared to period t.

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To be able to argue for an index to be operational, harm is needed to be quantified using numerical values. Kärrholm et al. (2020) is the first publicly published paper to in-depth discuss the different possibilities on how to derive a Swedish version of the Crime Harm Index. As Kärrholm et al. (2020) explains, a growing consensus recently has been to derive the index from law and sentencing outcomes. The exact method of how to derive the index is dependent on the context and legal systems within each specific country.

Originally, Sherman et al. (2016) derived the first Crime Harm Index, the Cambridge CHI, using sentencing guidelines. Using guidelines from England and Wales, they were able to derive the time of imprisonment for a first-time offender, excluding any aggravating or mitigating circumstances.

If lacking sentencing guidelines, as in the case of Sweden, other alternatives are needed. The important aspect when deriving the index, regardless of the method used, is that the index fulfills the criteria’s of democracy, reliability, affordability, validity, and operationality (Kärrholm et al., 2020)

By democratic means that the index should reflect the resolution of different conflicting parties’ viewpoints, through a democratic process. Further, the index should also be reliable in the sense that it is consistent over time, places, and individuals. This is crucial for comparing harm over time and between groups. The third criterion is the cost aspect. It should be a process of minimal costs to derive such an index and should be done with existing systems. The final two criteria are validity and operationality, which

concerns that the index should be measuring the harm objectively as well as be easily understandable without extensive background knowledge or information.

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metrics, and expert estimates. Sentencing data from all judges in all cases could be used to calculate the average sentences for each crime type. This alternative fulfills the majority of the criteria well. However, one cause of concern in the Swedish context is that there is no currently available data that distinguish first-time offenders from others. This makes the validity aspect a bit troublesome since first-time offenders are important to enabling an equivalent valuation.

The second alternative is the usage of the penal code. This could be done using the maximum, minimum, or average sentencing for each crime. Either is fine in the sense that they meet the requirements well and they all provide a measure of relative harm for each crime. Kärrholm et al. (2020) provide a discussion for the pros and cons for each of the three ways and concludes that the use of the average statutory sentence is the preferable way if choosing penal codes for deriving a Swedish CHI. The motivation for this was stated to be that the maximum percent variance was higher for the average sentence. The variance being key for the index to be useful.

The third alternative of deriving a good Swedish CHI discussed in Kärrholm et al.’s (2020), using expert estimates, is an alternative that has been done and applied to Swedish data. In Rinaldo (2015), judges were asked to provide an “expected verdict” for violent crimes conducted in public places. Using the answers, Rinaldo (2015) was the first to ever develop a Swedish Crime Harm Index (SCHI). This way of deriving a harm index also meets the criteria mentioned. Compared to Swedish sentencing data, judges can estimate the sentencing for a first-time offender. Also, comparing to the use of penal codes, judges’ estimates provide more specific and detailed

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In this thesis, great considerations have been taken to Kärrholm et al. (2020) comprehensive discussion for which alternative suits the context of Sweden best. Given the aim of the thesis, as well as the time constraints, using the judges’ estimations made by Rinaldo (2015) seemed the most plausible.

3.2 Applying the index to the setting of this thesis

In Rinaldo (2015), a summary of all crime classification codes together with a description as well as the corresponding expected verdict from all the judges was presented. Using these crime classification codes and descriptions current for 2015, an updated version using the crime codes and description for 2020 was produced. This was made using the yearly crime classification report, from The Swedish National Council for Crime Prevention (2021), in which updated crime classification codes are presented each year.

Out of the 74 crime classification codes and their description used in Rinaldo

(2015), 68 codes were identified as valid and still in use in 2020.1

For the remaining 68 codes, the constructed index value by the expert estimates in Rinaldo (2015) was applied (see Appendix A). The index represents the expected number of days in imprisonment for a first-time offender, estimated by the judging panel assigned by Rinaldo (2015). All crimes included in this thesis are categorized as different types of crimes against an individual in a public place, and span between for example murder, manslaughter, and molestation.

The reason for only including crimes against a person in a public place in this thesis is twofold. Firstly, for practical reasons, Rinaldo (2015) includes only these types of crimes and the expert judges have only provided verdict

1_{The excluded crime codes compared to Rinaldo (2015) can be seen in}

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expectations for these crimes. Secondly, and perhaps more importantly, for ethical concerns when working with spatial analysis containing specific coordinates, using only crimes reported in public places makes it much harder to derive individual information such as home addresses and names from the coordinates attached. This aspect was also crucial for me gaining access to the police records. Potential implications on results are discussed in final considerations.

An example is presented in Table 1, using classification code 0310, Murder,

manslaughter or assault with a fatal outcome without the use of firearm against women.

Table 1

Code Crime

description

Days SCHI Y.M.D Lowest

Y.M.D Highest Y.M.D 0310 Murder, manslaughter or assault with a fatal outcome without the use of firearm against women

5840 16.0.0 16.0.0 16.0.0

Table 1. An example from Appendix A, showing Rinaldo’s (2015) derivation of the SCHI for the offense assigned crime code 0310.

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One might argue that a potential problem of using the estimated verdicts from the judges in Rinaldo (2015) and applying it on 2020 years data, is the possible risk of outdated expectational verdicts. If there has been a drastic change in the expected verdict for a specific crime classification code during the last five years, that change would not be accounted for in this analysis and might give a cause of a less reliable and less valid index over time. However, looking at the official data on actual sentencing length for the crimes included in this thesis, no such drastic change has been seen in the average sentencing over the last couple of years in Sweden (The Swedish National Council for Crime Prevention, 2021). Hence, one would not expect any drastic changes in the expected verdict during this period either. This should strengthen the validity of our index.

4. Data and Methodology

In the following section, the data is presented. Additionally, the merging process of the different data sources is explained and further is also the methodological process of the spatial- and hedonic analysis discussed in detail.

4.1 Data

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After the initial contact and later signed confidentiality agreement, the data was received. The raw data covers the municipality of Stockholm with the period of January to December 2020 and consisted of 26 016 transactions in total. Each transaction contained information on the transaction date, contract price, price per square meter, coordinates, types of housing, building stories, apartment floor, number of rooms, building year, monthly fee, and indication on the presence of elevator and balcony.

Table 2

Table 2. Summary statistics. Own calculations.

Due to the use of only apartments as well as missing or uninterpretable data, the number of transactions was decreased to 14 460. Some of these

transactions were located in the same apartment building, hence they had identical coordinates. For simplicity reasons when later on conducting the needed spatial weight matrix, only one transaction at each coordinate was left included. By default, the software ArcGIS Pro keeps the first transaction by date. This meant that the final number of unique transactions included in the analysis reached 12 283.

Summary statistics

Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) Max

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As seen in Table 2, the average transaction price is 4 456 525 SEK with large variation, spanning between 1 195 000 SEK up to 20 million SEK. The average size of the apartments is 61 square meters with a minimum and maximum of 12 as well as 223 square meters, respectively. The number of rooms of the sold apartments is on average 2.4 within the sample and the average building year is 1955.

Providing the data of the reported crimes is the Nationella Operativa

Avdelningen (NOA) within the Swedish police authorities. The first contact with the police was established through a sent in official request of a public act extraction. The data was later received from the police authority after some communication through phone and email, explaining the intended use of the data.

The data consists of several different types of crimes reported against individuals in public places, located within the metropolitan region of Stockholm, spanning the time period of first of January 2020 to last of December 2020 (see Appendix A). The total number of reports equaled 18 923. Out of these, 1 468 had missing coordinates and were excluded directly. The study area for this thesis is Stockholm municipality, hence all reports outside this area were excluded. The final number of reports used in the empirical analysis reached 8 662 in total and included all reported crimes against a person in a public space recorded within the borders of the

municipality of Stockholm.

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4.2 Methodology

To merge the cross-sectional data from Svensk Mäklarstatistik with the data from NOA, and finally, with the geographical data from Stockholm stad, the software ArcGIS Pro was used. ArcGIS Pro is a geographical information system (GIS) software, that enables advanced spatial analysis to be conducted.

The first step was to import the data from Svensk Mäklarstatistik and NOA containing coordinates for all apartment transactions as well as all the

reported crimes into the ArcGIS software. This was followed by inputting the geographical data from Stockholm stad.

Figure 1. ArcGIS Pro map post-merging of the different data sources.

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represents a reported crime. Included in each star is the date of the crime, the code of the crime, a description as well as the corresponding crime harm index for that specific crime code, taken from Rinaldo (2015). Each train marks out the coordinates of a station, included types are subway, shuttle as well as tram. The schools mark the placements of all public schools. Further are all highways and the water areas in direct connection to the municipality of Stockholm included. Lastly, the geographical borders represent the administrative borders of each area within the municipality of Stockholm. The municipality of Stockholm consists of 117 different administrative areas in total. This finalizes the step of merging all the data sets into ArcGIS Pro. Secondly, to make use of all the merged data and to enable the spatial analysis, each apartment transaction had to get its own assigned value

depending on its spatial relationship to its surrounding. Additionally to all the attribute data, each apartment therefore also received a value on its relation to schools, stations, roads, and water. This was done through the use of the multiple buffer analysis tool in ArcGIS. The tool creates custom-made ring buffers around the location of the different schools, stations, roads, and water shorelines. This enables measurement of each individual transaction’s

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Figure 2. Buffer analysis here seen performed on schools.

Finally, working with spatial data like this forces us to address the potential bias experienced from spatial dependence. Failing to control for this

endogeneity will much likely result in spatial autocorrelation in the residuals of a standard OLS, violating the basic assumption of normally distributed errors in the regression (Collins et al., 2006). The spatial autocorrelation arises from when one observation at one location is depending on the observations in nearby locations and would, for example in the case of criminal activity, mean that crime in one location very well might generate

spill-over effects on nearby locations (Ceccato and Wilhelmsson, 2011).

There are commonly two types of spatial dependence, that is the spatial error and spatial lag. Spatial dependence through the error term reflects the

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area i is affected by the independent variables in both i and neighboring area

j. If unaddressed, this spatial lag might result in both biased and inefficient

estimates (Piquero and Weisburd, 2010).

The existence of spatial dependence can easily be visualized in our data. In figure 3, the mean harm index is calculated for each administrative area. Even without conducting any formal statistical test, clear signs of

dependency are present. Areas with low mean CHI tend to cluster together and vice versa.

Figure 4 shows the aggregated harm, summing up the harm from every individually reported crime within each administrative area. This also shows clear tendencies of clustering, unsurprisingly with the highest aggregated harm at the inner-city areas.

To account for this spatial dependence, a weight matrix was created in the software package GeoDa. First off, each transaction was with the help of ArcGIS transformed from points into Thiessen polygons. These polygons were transferred into GeoDa which generated a weight matrix which in turn enabled the use of spatial models. The matrix created took the spatial structure of a Queen’s matrix, with the contiguity of order one. Objects are hence classified as neighbors if they share a common edge or vortex, receiving a 1 in the matrix, 0 otherwise.

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Figure 3. The area mean harm for all 117 administrative areas.

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Figure 5. The mean selling prices for all 117 administrative areas.

Figure 5 categorizes the administrative areas according to their mean transaction prices. Higher prices show clear signs of clustering within and around the inner city.

Using the constructed weight matrix, a statistical test called Moran’s I, one of the most common tests for spatial autocorrelation was performed. The

Moran’s I rejected the null hypothesis of no autocorrelation. The test suggested the presence of strong spatial autocorrelation, both for harm, as well as transaction prices. The Moran’s I tests confirm what was already expected. There is a strong need of taking spatial autocorrelation into account when performing the hedonic price regressions.

4.3 The Hedonic price equation

The process of determining an individual’s willingness-to-pay for housing is without doubt complex. Additionally of taking into account all the

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monthly fees, and waterfront view or not, the buyer will also look at the features of the closest surrounding neighborhoods to the object (Thaler, 1978).

What it comes down to in its simplest form is the following equation:

𝑝 = 𝑿𝛽 + 𝜀 (1)

where p is the housing price, normally in log-form, X is a matrix containing all attributes that possibly might influence the price and where 𝛽 is the corresponding vector to each attribute, measuring the marginal implicit price of that specific attribute. It might not look like such a struggle to estimate but there are some hidden and large challenges.

First of all, knowing which attributes and characteristics that are relevant to include is not that straightforward. There is for obvious reasons not plausible to include every thinkable determinant for prices since individuals’

preferences are different in so many ways. Actually, no real consensus has been established in the previous literature regarding which factors that preferably should be included. When it comes to the actual attributes of the buying object, most papers however agree that factors such as living area, the number of rooms, monthly fee, and plot size, etc. should be included. When it comes to the attributes of the surrounding area, there is less of an agreement.

Environmental aspects are surely an influential determinant of price. Having a waterfront nearby is normally associated with higher prices while being close to a heavy industry might be expected to lower the price in general (Ceccato and Wilhelmsson, 2011).

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parks differs with respect to the level of crime in the area. In low crime neighborhoods, having an urban park positively affects the willingness-to-pay, while for neighborhoods with high crime rates, the effect goes in the opposite direction. Kane, Riegg, and Staiger (2006) show similar

heterogeneous effect on the willingness-to-pay from being in close proximity of different schools, and Bowes and Ihlanfeldt (2001) show heterogeneity in the effect of railway stations depending on income levels and distance to the inner city.

As a consequence of the above, there has been a consensus developing among researchers that there is a need of dividing the housing market into sub-markets. This consensus originates from that different features have different demands over space. This makes the implicit price of these futures to also differ. For example, as income levels change, so does the implicit price of neighborhoods with low crime. Ceccato and Wilhelmsson (2011) argue that the price of having a low crime neighborhood should be higher in areas with many crimes, such as the inner city.

Further, Ekstam and Sandstedt (2010) suggest that differences in individuals’ life-style and the composition of the households might make the tolerance level towards crime heterogenous among sub-markets. To actually divide a large housing market into sub-markets may however be problematic,

addressed by previous research such as (Wilhelmsson, 2004); (Goodman and Thibodeau, 1998), further stressing the complexity when researching on the subject.

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Adopting this hedonic price equation to fit this thesis, by including a variable of crime harm, enables us to estimate how much buyers would be willing to pay to avoid criminal harm. We state the hedonic price equation as follows:

𝑝 = 𝛼 + 𝛽𝑿 + 𝛾ℎ + 𝜀 (2)

where p is a vector containing the observations of housing prices, normally in log form. 𝛽 is a vector of coefficients corresponding to the exogenously explanatory variables in matrix X. X is a matrix containing all housing attributes, together with the attributes of the geographical surroundings. In this thesis specifically, that means that X contains all the data from Svensk Mäklarstatistik as well as from the Stockholm open database for GEO data. The vector 𝛾 contains the coefficients associated with the h vector,

containing the administrative area mean CHI measure. Since the variable is an index, it will be standardized and hence 𝛾 will estimate the marginal willingness-to-pay for a change with one standard deviation in the area mean CHI.

The most crucial assumption for the validity of the model estimates is that 𝑿 and ℎ are exogenously given, which also is the hardest assumption to fulfill. Potential reasons for the assumption not to hold might primarily be omitted variables or measurement errors, and of course as already mentioned, spatial dependence. Further, reverse causality is an additional reason for a possible violation of the assumption.

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To address the spatial dependence two additional equations can be estimated using the earlier created weight matrix. To be able to choose the right control for spatial dependence, we need to understand what causes the dependence. As previously mentioned, one potential cause for the dependence is that spatial autocorrelation has arisen from spatially autocorrelated omitted variables that affect the dependent variable. The other alternative is that of when spatial autocorrelation originates from endogenous dependent variables (Bernasco and Elffers, 2010).

If the autocorrelation is argued to be coming from omitted variables the spatial error model (SEM) is usually preferred. SEM uses the weighting matrix to split the error term into one spatially dependent and one that is not. SEM takes the following form:

𝑝 = 𝛼 + 𝛽𝑿 + 𝛾ℎ + 𝜆𝑾𝜀 + 𝜇 (3)

where 𝜀 is an error term vector experiencing spatial dependence, which structure is specified by W, the weighting matrix. 𝜆 is a single parameter showing the level of spatial interaction. 𝜇 is the remaining non-spatial dependent error term.

If instead the autocorrelation is suspected to be coming from that the dependent variable itself is influenced directly from the neighboring locations, the spatial lag model (SLM) is preferred.

SLM includes the lagged dependent variable in the regression equation and looks the following:

𝒑 = 𝛼 + 𝛽𝑿 + 𝛾𝒉 + 𝜌𝑾𝒑 + 𝜀 (4)

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(Anselin et al, 1996). In table 3, the data shows highly significant values for both the LM error as well as the LM lag model. As a consequence, from only these two tests, no choice of the model specification can be made.

Following the guidelines from Anselin (2004) when faced with this situation, attention is instead moved towards the robust versions of the test. Looking in table 3, the Robust LM error statistics come back highly significant while the Robust LM lag statistic is not.

Therefore, from the results of the diagnostic test in table 3, we are fairly confident that the spatial error model is the right choice to tackle the spatial dependency in this dataset. Additionally, to further help to distinguish

between the models fit, some guidance can be found in the primary empirical aim of the study.

Table 3

LMerr = 7953.9 df = 1 p-value < 2.2e-16

LMlag = 2329.5 df = 1 p-value < 2.2e-16

RLMerr = 5626.9 df = 1 p-value < 2.2e-16

RLMlag = 2.3971 df = 1 p-value = 0.1216

Table 3. Lagrange multiplier diagnostics for spatial dependence.

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strengthens our choice of using the spatial error model. Leaving the analysis of the actual strength of the spatial interaction to future research.

5. Results

Looking in Table 4, starting in the simple OLS model (1), the main variable of interest Area Mean CHI in this first specification shows no sign of significance. For interpretation reasons, the variable Area Mean CHI is standardized, i.e. the mean value is subtracted from the value for each individual case, resulting in a mean of zero. Further is the resulting

difference divided by the standard deviation, resulting in a standard deviation of one. This means that the Area Mean CHI coefficient in (1) should be interpreted in the sense that an increase of one standard deviation in the Area

Mean CHI will decrease prices by .01 percent.

There is in (1), seemingly no statistical evidence for a relationship between housing prices and the mean CHI in the administrative area. There are, however, as explained earlier, several possible reasons why the results here should be treated with large skepticism.

First of all, we know that the data suffer from spatial dependence, present through the highly significant spatial autocorrelation in the area mean CHI. Our residuals will be spatially autocorrelated, hence violating one of the most basic assumptions of an OLS regression. Secondly, we have in no form or way, controlled for any sort of heterogeneity in space. As discussed, this heterogeneity in space could for example be due to some differences in crime tolerance levels between districts, meaning that changes in the area mean CHI, might impact prices differently across spaces. Additionally,

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Table 4. Hedonic price regressions. Table 4 Log Price OLS Spatial error model (1) (2) (3) (4)

Area Mean CHI -0.0001 -0.0004 -0.005** _-0.003**

(0.001) (0.001) (0.002) (0.001) Apartment floor 0.008*** 0.007*** 0.007*** 0.007*** (0.001) (0.0004) (0.0003) (0.0003) Building stories 0.004*** 0.001** -0.00004 -0.00004 (0.001) (0.0003) (0.0004) (0.0003) Living area 0.007*** 0.005*** 0.005*** 0.005*** (0.0001) (0.0001) (0.0001) (0.0001) Number of rooms 0.019*** _0.018*** _0.016*** _0.016*** (0.002) (0.002) (0.001) (0.001) Build year -0.002*** _-0.001*** _-0.0002*** _-0.0003*** (0.00003) (0.00002) (0.00003) (0.00003) New product 0.098*** _0.044*** _0.004 _0.008 (0.013) (0.008) (0.008) (0.008)

Log Monthly fee -0.271*** _-0.058*** _0.051*** _0.038***

(0.009) (0.006) (0.006) (0.006) Elevator 0.047*** _0.006*** _0.002 _0.002 (0.002) (0.002) (0.001) (0.001) Balcony 0.001 0.007*** _0.013*** _0.012*** (0.002) (0.001) (0.001) (0.001) Water100 0.134*** _0.047*** _0.039*** _0.027*** (0.004) (0.003) (0.007) (0.005) Water300 0.069*** _0.019*** _0.024*** _0.013*** (0.003) (0.002) (0.006) (0.004) Water500 0.053*** _0.018*** _0.014*** _0.009*** (0.003) (0.002) (0.004) (0.003) Highway100 -0.024** _-0.052*** _-0.021** _-0.042*** (0.010) (0.006) (0.010) (0.008) Highway300 0.020*** -0.033*** -0.011 -0.030*** (0.004) (0.003) (0.007) (0.005) Highway500 0.012*** _-0.028*** _-0.004 _-0.019*** (0.004) (0.003) (0.005) (0.004) School100 0.038*** _-0.012*** _-0.001 _-0.007 (0.005) (0.003) (0.006) (0.005) School300 0.025*** _-0.012*** _-0.001 _-0.006 (0.004) (0.003) (0.005) (0.004) School500 0.002 -0.013*** _-0.003 _-0.007* (0.004) (0.003) (0.004) (0.004) Station100 0.053*** _0.032*** _0.016*** _0.026*** (0.005) (0.003) (0.005) (0.004) Station300 0.053*** _0.036*** _0.008** _0.020*** (0.003) (0.002) (0.004) (0.003) Station500 0.039*** _0.027*** _0.006* _0.015*** (0.003) (0.002) (0.003) (0.003) Constant 10.090*** _7.491*** _6.525*** _6.755*** (0.061) (0.047) (0.059) (0.055)

Fixed effects No Yes No Yes

Observations 12,283 12,283 12,283 12,283

R2 _0.691 _0.870

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In the second OLS specification, district fixed effects are added in a try to account for the heterogeneity in space. However, after controlling for district fixed effects our variable of interest Area Mean CHI is still insignificant. I.e. measuring the relation between increased area mean CHI and apartment prices within districts, holding district-specific characteristics constant, do not change the estimates of the implicit willingness-to-pay much other than for the apartment- as well as geographical attributes.

The resulting estimates differ slightly when comparing with the first specification. In general, most of the attribute variables have decreased estimates. For the distance to the nearest school, the estimates have switched signs completely. Having increased price as in (1), being close to a school now decreases price after introducing district fixed effects in (2). The estimate that otherwise differs the most is the monthly fee, from -.27 to almost -.06. The latter which arguably is more in line with expectations compared to previous literature.

In the third specification, the spatial error model is estimated using equation (3). The results differ quite substantially from the two previous OLS

specification.

The apartment attributes are estimated fairly consistent with the previous specifications, but the geographical variables are to a larger extent

insignificant in (3). In other words, using the spatial error model, controlling for the spatial dependence in our data through capturing possible spatially influencing omitted variables, lowers the significance of our included geographical variables.

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that ideally would be attributed to the geographical variables, hence experiencing multicollinearity.

However, the most important difference, for the aim of this thesis, is that the estimate of the variable Area Mean CHI is now significant. The coefficient of -.005 suggests that an increase with one standard deviation in the

administrative area mean CHI value will estimate a decrease in prices with .5%.

To get some context, what the coefficient really suggest is the following: An apartment sold in an administrative area, with an area mean CHI equal to the total average of all the 117 included areas, would be estimated to sell for 2.6% less, if instead sold in an administrative area with one of the highest area mean CHI, all else equal.

Two administrative areas that fit the example above are Hässelby Strand and Beckomberga. Converting this example into monetary value, this would predict an apartment sold in Hässelby Strand for the sample mean price of around 4.5 million SEK, to be selling at 117 000 SEK less if moved to the administrative area of Beckomberga. A very much non-negligible effect. An alternative interpretation of the resulting coefficient for Area Mean CHI is that an apartment sold in an administrative area with the ‘total harm’ as well as the ‘number of reported crimes’ equal to the mean values of

Stockholm, will be estimated to sell for .17% less, if an additional murder is added to that area, all else being equal. In monetary value for an apartment sold at the sample mean price, this would equal around an 8 000 SEK

decrease in price for one additional murder in the administrative area. Similar calculations could be made to predict the effect on apartment prices for each and every individual crime type included in the CHI.

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specification (2), we now control for all factors constant to each district, in other words, the effect of a change in the area mean CHI is measured within each district.

The coefficient for Area Mean CHI in this fourth specification equals -.003. Compared to specification (3), this coefficient now suggests that the earlier example apartment sold for the sample mean price in Hässelby Strand, would be estimated to sell for 1.56% less (or 70 200 SEK), all else equal, if moved to Beckomberga. A smaller, but still a non-negligible effect.

According to the alternative interpretation, in which we added an additional murder to the area of the apartment, instead of as in specification (3)

estimating a decrease in price of .17%, specification (4) estimates a decrease of .10%. In monetary value, this equals around 4 700 SEK decrease in selling price adding an additional murder to the administrative area.

Monte-Carlo simulations were performed of the Moran’s I after estimating both the spatial error models. Simulations showed no significantly persisting spatial autocorrelation in the residuals in neither of the two spatial models. This is crucial for the validity of the results and strengthens the confidence of having efficiently estimated coefficients.

6. Final considerations

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Acknowledging the relative harm of different crimes could according to Cohen (1990) be crucial in the sense that areas with similar crime rates might differ substantially in public safety. This is a strong argument for the

usefulness and potential need of a weighting index like the CHI.

To the best of my knowledge, despite Cohen’s (1990) early suggestions, only ones, have a similar weighting of criminal offenses been used in the past literature. It was done all the way back in 2001 by Lynch and Rasmussen (2001) in a criticized attempt that found no significant relation to housing prices.

Interestingly, this is not the case in this thesis.

A strong significant relationship between the area mean harm and apartment prices can be found in both specification (3) and (4), and the coefficients estimate negative effects of increased area mean harm on apartment prices. Moving an apartment from an administrative area with a level of area mean harm in accordance with the average for Stockholm, to an area with one of the highest levels of area mean harm, decreases prices by 2.6%. For an apartment sold at the average price of this sample, this equals a decrease of around 117 000 SEK using specification (3). Very much a non-negligible effect.

However, giving a definite answer to the established research question of whether or not the use of the CHI measure estimates the costs of crime on housing prices differently to previous crime rates and hot-spots, turns out to be complex.

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However, ideally, we would also have liked to compare the actual magnitude of this negative relation, but it is hard since the way of estimation, as well as interpretation, differs in the literature. For example, Ceccato and

Wilhelmsson (2020) focused on distance from crime hot-spot and established that moving a house one kilometer further away from a hot-spot increased price by more than 30 000 SEK. Ceccato and Wilhelmsson (2011) instead interpret their results in elasticities, finding that if the crime rate in

Stockholm increased by 1%, housing prices decreased by .04%.

Additionally, the results of this thesis could further act as an illustrative example of the complexity and heterogeneity incorporated into the research field of the relationship between crime and housing prices. Calculations show that, for an administrative area with a given Area Mean CHI value, the effect that an additional crime will have on apartment prices, is partly

depending on the area’s ‘total harm’ value. The larger the relative increase an added crime brings to the area’s ‘total harm’, the larger effect on prices it will have. This implies that if having two administrative areas with equal

Area Mean CHI, the area with the lowest ‘total harm’ value of the two, will

experience a larger negative effect on apartment prices from two identical crimes added.

Further, we can also utilize the weighting approach which this CHI provides, enabling us to more easily estimate the monetary effect of a single specific crime type on apartment prices. We can hence differentiate between the costs of different crimes. In the bigger picture and in theory, this would imply that, as long as a valid CHI value could be assigned to a different crime type, we could not only estimate precise costs of different criminal activity on the housing market but also help to estimate the societal cost of different crime type.

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this thesis should be large. This should especially be true for actors such as urban planners and policymakers for good decision-making regarding security investments and resource allocation.

The result in this thesis is however not without limitations.

Even though the spatial error model works seemingly fine in countering the spatial autocorrelation as suggest by the Moran’s I simulations, the resulting estimates of this thesis should still be taken with some precautions. Two primary reasons for this suggested precaution are identified.

Firstly, given the early discussion regarding the two different types of spatial dependency, the dependence through spatial errors reflected the situation in which our estimates were being inefficient estimated, although still unbiased. The use of the spatial error model is therefore primarily expected to change the efficiency of our estimates. However, in this thesis, the actual coefficients themselves differ quite substantially when comparing the OLS specifications in (1) and (2) to our spatial error estimates in (3) and (4). Liv Osland (2010) argues that if this is the case, it could be an indication of model

misspecification. This should be investigated further in future studies. Secondly, there is still evidence of persistent spatial heterogeneity in the models. Even after controlling for fixed effects in specification (4), measuring the relation between area mean harm and prices within the different districts of Stockholm, heterogeneity in space is present and hence our estimate precision could be questioned. There might be a need for more specified sub-markets.

Further, what also should be considered is the fact that only crimes against a person, and conducted in public places, are included in the CHI, as

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for bias in the resulting estimates. Especially so, if there for an administrative area, are substantial differences regarding the number of crimes as well as the severity of the crimes conducted in public places versus crimes

conducted at home addresses.

Similarly, it is crucial to acknowledge that the analysis in this thesis is

conducted on only apartment prices. This might give cause of some problems with external validity. The resulting estimates presented in this thesis, should hence not be generalized to other properties such as houses, as homeowners and apartment owners might differ in other regards, impacting their response to increased crime et cetera.

Further, what also should be acknowledged is the risk of reverse causality coming from the situation when apartment prices are affecting criminal activity. Even though violent crimes, as are being used in this thesis have shown less tendency towards being affected by housing prices as discussed in Ceccato and Wilhelmsson (2011), compared to for example burglaries, it could still potentially be an issue.

Additionally, since the area mean CHI value is calculated from the reported crimes within an administrative area, there could be some causes of concern regarding the assigning of reported crimes between areas. Especially as to when a serious crime with a high CHI value is committed right on the border for two areas. The same goes for when an apartment is right on the

borderline between two administrative areas with different area mean CHI values. However, what should be seen as a mitigating factor for this

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Also important for the resulting estimates is the timing aspect. It could be of interest for future research to make use of a lagged approach. It may be reasonable to suggest that there is a delay between the time of a reported crime and the effect on prices. Potential ways to account for this would be to use longitudinal data in which effects over time would be possible to

estimate. Such delay is not acknowledged in this thesis due to data limitations.

Closely connected to the timing aspect, is the buyer’s actual knowledge of the reported crimes. Less severe crimes might not make any headlines in the media and different crimes might hence influence the perceived safety differently. If buyers do not have full insights into the surrounding crime level of an apartment, the estimates could be biased. This is something that will be crucial for future studies to expand on.

However, given the incipient nature of this severeness weighting approach, limitations to the results of this thesis were expected. The identified

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Appendix A

Swedish Crime Harm Index (SCHI)

Source: Rinaldo, M. B. V. (2015). Comparing crime hotspots and crime harm-spots

in a Swedish City: a descriptive analysis. England: Cambridge University.

Code Crime description Days SCHI Y.M.D Lowest Y.M.D Highest Y.M.D

0310 Murder, manslaughter or

assault with a fatal outcome without the use of firearms against woman

5840 16.0.0 16.0.0 16.0.0

assault with a fatal outcome without the use of firearms against man

5840 16.0.0 16.0.0 16.0.0

assault with a fatal outcome with the use of firearms against woman

6570 18.0.0 18.0.0 18.0.0

assault with a fatal outcome with the use of firearms against man

6570 18.0.0 18.0.0 18.0.0

0355 Physical abuse, other

than gross, against woman 18 years or older, unfamiliar with the victim, outdoor

60 0.2.0 0.2.0 0.2.0

0357 Physical abuse, other

than gross, against man 18 years or older, unfamiliar with the victim, outdoor

60 0.2.0 0.2.0 0.2.0

0375 Physical abuse, gross,

against woman 18 years or older, unfamiliar with the victim, outdoor

492 1.4.7 1.3.0 1.6.0

0377 Physical abuse, gross,

against man 18 years or older, unfamiliar with the victim, outdoor

492 1.4.7 1.3.0 1.6.0

9447 Unlawful threat against

man 18 years or older

30 0.1.0 0.1.0 0.1.0

9443 Unlawful threat against

woman 18 years or older

30 0.1.0 0.1.0 0.1.0 9463 Molestation of man 18 years or older 14 0.0.14 0.0.14 0.0.14 9459 Molestation of woman 18 years or older 14 0.0.14 0.0.14 0.0.14

0451 Unlawful threats against

girl under 18

30 0.1.0 0.1.0 0.1.0

0453 Unlawful threats against

boy under 18

30 0.1.0 0.1.0 0.1.0

0428 Molestation of girl under

18

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0429 Molestation of boy under 18 14 0.0.14 0.0.14 0.0.14 0440 Unlawful persecution of girl under 18 292 0.9.22 0.6.0 1.0.0 0441 Unlawful persecution of boy under 18 292 0.9.22 0.6.0 1.0.0 9427 Unlawful persecution of

woman 18 years or older

183 0.6.0 0.6.0 0.6.0

9431 Unlawful persecution of

man 18 years or older

183 0.6.0 0.6.0 0.6.0

0640 Attempted rape incl.

gross, against girl under 15 years, outdoor

1460 4.0.0 4.0.0 4.0.0

gross, against boy under 15 years, outdoor

1460 4.0.0 4.0.0 4.0.0

gross, the woman 18 years or older, outdoor

1095 3.0.0 3.0.0 3.0.0

gross, the man 18 years or older, outdoor

1095 3.0.0 3.0.0 3.0.0

0652 Consummated rape incl.

gross, against girl under 15 years, outdoor

1971 5.4.26 5.0.0 6.0.0

gross, against boy under 15 years, outdoor

1971 5.4.26 5.0.0 6.0.0

gross, against woman 18 years or older, outdoor

1460 4.0.0 3.0.0 5.0.0

gross, against man 18 years or older, outdoor

1460 4.0.0 3.0.0 5.0.0

gross (§ 1), against girl 15 -17 years, outdoor

1205 3.3.20 3.0.0 3.6.0

gross (§ 1), against boy 15 -17 years, outdoor

1205 3.3.20 3.0.0 3.6.0

2044 5.7.9 5.0.0 6.0.0

1533 4.2.13 3.0.0 5.0.0

gross (§ 4), against boy 15 -17 years, outdoor

1533 4.2.13 3.0.0 5.0.0

1606 4.4.26 3.0.0 6.0.0

gross (§ 4), against boy 15 -17 years, outdoor 1606 4.4.26 3.0.0 6.0.0 0892 Robberies without firearms against a private individual, functional impairment, outdoor 730 2.0.0 2.0.0 2.0.0

0896 Robberies with firearms

against a private

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individual, functional impairment, outdoor

9301 Physical assault, not

gross, against girl 0-6 years, unfamiliar with the victim, outdoor

144 0.4.24 0.3.0 0.6.0

gross, against girl 0-6 years, familiar with the victim, outdoor

144 0.4.24 0.3.0 0.6.0

gross, against boy 0-6 years, unfamiliar with the victim, outdoor

144 0.4.24 0.3.0 0.6.0

gross, against boy 0-6 years, familiar with the victim, outdoor

144 0.4.24 0.3.0 0.6.0

90 0.3.0 0.2.0 0.4.0

78 0.2.18 0.2.0 0.3.0

72 0.2.12 0.1.0 0.3.0

9325 Physical assault, gross,

against girl 0-6 years, unfamiliar with the victim, outdoor

1241 3.7.26 2.0.0 4.0.0

against girl 0-6 years, familiar with the victim, outdoor

1241 3.7.26 2.0.0 4.0.0

against boy 0-6 years, unfamiliar with the victim, outdoor

1241 3.7.26 2.0.0 4.0.0

against boy 0-6 years, familiar with the victim, outdoor

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9333 Physical assault, gross, against girl 7-14 years, unfamiliar with the victim, outdoor

985 2.8.15 1.6.0 3.0.0

against girl 7-14 years, familiar with the victim, outdoor

985 2.8.15 1.6.0 3.0.0

against boy 7-14 years, unfamiliar with the victim, outdoor

985 2.8.15 1.6.0 3.0.0

against boy 7-14 years, familiar with the victim, outdoor

985 2.8.15 1.6.0 3.0.0

against girl 15- 17 years old, unfamiliar with the victim, outdoor

620 1.8.15 1.0.0 2.0.0

against girl 15- 17 years, familiar with the victim, outdoor

620 1.8.15 1.0.0 2.0.0

against boy 15- 17 years old, unfamiliar with the victim, outdoor

620 1.8.15 1.0.0 2.0.0

against boy 15- 17 years, familiar with the victim, outdoor

620 1.8.15 1.0.0 2.0.0

9806 Robbery against an

individual, not functional impairment, under 18 years, without firearms, outdoor

365 1.0.0 1.0.0 1.0.0

9808 Robbery against an

individual, not functional impairment, under 18 years, with firearms, outdoor 584 1.7.9 1.0.0 2.0.0 9810 Robbery against an individual, not functional impairment, 18 years or older, without firearms, outdoor 365 1.0.0 1.0.0 1.0.0 9812 Robbery against an individual, not functional impairment, 18 years or older, with firearms, outdoor

584 1.7.9 1.0.0 2.0.0

9819 Theft, shoplifting

without burglary, handbag snatching from non-disable person

183 0.6.0 0.6.0 0.6.0

9820 Theft, shoplifting

without burglary, handbag snatching from disable person

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Excluded crime codes compared to Rinaldo (2015) are:

0356 - physical abuse, other than gross, against woman 18 years or older,

The importance of crime severity for housing prices