Neighbourhood income inequality and property crime

Abstract

Chinese

This paper examines the relationship between income inequality and property crime using Census block group data from three US cities: Nashville, TN, Portland, OR and Tucson, AZ. This paper is one of very few to examine this relationship at such a fine geographic level, which is typically less than one square mile in size. We find that income inequality across block groups plays a key role in determining the level of property crime. As the income gap with one’s poorest neighbouring block group widens, the level of property crime in the richer block group increases. Also, the poorest block group in an area tends to experience less property crime, holding all else constant.

Keywords

crime geographic information systems (GIS)income inequality

Introduction

Theory indicates there is an important link between income inequality and crime (Becker, 1968). According to Becker’s economic theory of crime, the relative benefits of committing a crime are greater in communities with greater income inequality compared with those with a more even income distribution. Thus, as the benefits to crime increase, holding all else equal, the level of crime increases. Ehrlich (1973) expanded upon Becker’s theory by arguing that low-income individuals have a greater incentive to pursue illegal activities when surrounded by greater wealth. It is worth nothing that Becker’s and Ehrlich’s work does not distinguish between property and violent crime.

Chiu and Madden (1998) provide a theoretical explanation for the link between income inequality and property crime, such as burglary. Their work demonstrates that an increase in income inequality leads to an increase in the number of burglaries across a set geographical area and that crime levels may be higher in richer neighbourhoods. This result is driven by the idea that as the income gap widens, rich households become more attractive targets for low-income burglars. Thus, the possible benefit from crime is increasing while the cost from imprisonment is unchanged which leads to an increase in property crime. Their theory on property crime provides motivation for the empirical model we estimate in this paper.

Empirical studies examining the relationship between inequality and crime return mixed results based on the type of crime committed. Studies on violent crime generally agree that greater income inequality leads to an increase in violent crime (Daly et al., 2001; Doyle et al., 1999; Kang, 2014; Kelly, 2000). Studies examining the impact of inequality on property crime show no effect (Allen, 1996; Bourguignon et al., 2003; Kelly, 2000; Neumayer, 2005), a positive effect (Choe, 2008; Demombynes and Ozler, 2005; Whitworth, 2013; Wilkinson and Pickett, 2006), or a negative effect (Brush, 2007; Kang, 2014). These results differ based upon the geographic level of observation. Studies using country- or state-level data usually find a positive relationship between inequality and property crime (Choe, 2008; Fajnzylber et al., 2002). However, those using smaller scale data at a county or city level return mixed results (Entorf and Spengler, 2000; Kelly, 2000). The lack of a consistent result between income inequality and crime is plausibly due to the modifiable area unit problem (MAUP) which has been an issue of interest in spatially oriented social research for decades. Weisburd et al. (2008) explore the issue of crime and geography in great depth, and in particular discuss MAUP. In choosing a geographic level to examine data, two possible problems arise. First, the unit of analysis may mask the true relationship between the variables of interest. That is administrative boundaries, such as Census boundaries, may not define neighbourhoods properly and thus a true neighbourhood or cluster of crime may overlap a Census boundary. Second, the level of aggregation may play an important role in the results. An analysis of crime at the Census tract level versus a group of Census tracts (much larger area) can return quite different results (Ouimet, 2000). Weisburd et al. (2008) suggest that ideally one would use small areas as a unit of observation to address the aggregation issue and choose area boundaries which accurately reflect important spatial patterns for a specific study.

Owing to the lack of consistent results for inequality and property crime, we further examine the relationship in an attempt to clarify the ambiguity in the current findings. Property crime, as opposed to violent crime, is of particular interest as income differences may create strong economic incentives to commit property crime. This paper uses Census block group data to explore the relationship between income inequality and property crime. A Census block group is typically one square mile in size and is the smallest geographic level for which the Census publishes income data. We use small-scale data as most crimes are committed on a local level and criminals typically travel very short distances, between one and two miles, to commit crimes (Wiles and Costello, 2000). Block group data also allow us to address the aggregation issue discussed by Weisburd et al. (2008), as country-, state-, county- or city-level data may be geographically too large if one wants to accurately determine the nature of the relationship between income inequality and crime.

While small-scale data allow one to examine crime differences at a local level, it creates issues as well. At large scales, criminals are assumed to commit crimes within their own country, state, county or city. However, at the block group level it is very likely criminals are committing crimes not only within their own block group, but also in neighbouring block groups. Cohen and Felson’s (1979)‘routine activity’ theory suggests that crime is more likely to take place when conditions are conducive to crime, and that the offenders commit crimes in places with which they are most familiar, such as on the way to work or while doing other activities. Hirschfield and Bowers (1997) argue that offenders are more tempted to commit a crime when they have daily contact with people who are more fortunate. Moreover, the attractiveness and accessibility of surrounding neighbourhoods motivate burglars to explore crime opportunities in neighbourhoods outside of their own (Bernasco and Luykx 2003). These theories indicate the need to account for income inequality within and across block groups.

Throughout economic literature income inequality is most commonly measured by the Gini coefficient. In the crime literature several measures of inequality have been used, the Thiel Index, Atkinson Index, Concentration at the Extremes Index, and most commonly the Gini coefficient (Roberts and Willits, 2015). The important aspect of these inequality measures is that they measure inequality within a single geographic area, but do not capture the income differences across geographic areas. As the scale of observation becomes smaller, one must directly account for the inequality across areas as it likely plays an important role in describing the location of property crime.¹ An important recent study to mention is Whitworth (2013), which uses the Gini coefficient to study the relationship between income inequality and crime at a small geographic level. The results indicate little to no relationship between income inequality and property crime, which could be explained by the lack of inequality measures across areas at this geographic level. In Whitworth (2013), the Gini coefficient measure is calculated over increasingly larger spatial areas, but the Gini coefficient makes no distinction between income inequality in the focal area, where the crime occurs, and the surrounding neighbourhood areas. Our study, much like Whitworth (2013), is interested in the localised relationship of income inequality and crime. However, we examine the performance of the Gini coefficient within a block group and more importantly construct additional measures of income inequality across groups.

Another issue when examining crime at small geographic areas is that high crime rates tend to cluster because of a spillover effect (Bernasco and Elffers, 2010; Tobler, 1970; Zhang and Song, 2013; Zhao et al., 2014). Most papers studying crime and income inequality at a small geographic level have used correlation analysis (e.g. Demombynes and Ozler, 2005; Entorf and Spengler, 2000; Witt et al., 1999), and thus did not account for the spillover effect which could lead to biased estimates. We address this issue by employing a spatial regression model, which accounts for spatial autocorrelation of crime and other unobservable characteristics. The use of spatial modelling is expected to produce more accurate estimates for the relationship between income inequality and property crime.

Using property crime and Census data from Nashville, TN, Portland, OR and Tucson, AZ, our paper evaluates the relationship between income inequality and property crime. Our study contributes to existing literature by conducting analysis at the block group level which employs improved measures of inequality across neighbouring units, and accounts for the spatial correlation of property crime and other unobservables. To our knowledge, this study is the first to focus on property crime and income inequality at the block group level, which is the smallest geographic scale at which income data is available. While small scales have issues, it is important to note that criminals often travel short distances (1–2 miles) and thus for property crime, income variation at this small scale is necessary to accurately explain the relationship. The results of our analysis indicate that as the income gap with one’s poorest neighbour increases, property crime in one’s own block group increases. We also find that the poorest block group relative to its neighbours tends to have lower property crime rates. Finally, we find that within a block group the Gini coefficient has little explanatory power in the level of property crime.

Data

We obtained the data used in this study from several sources. Property crime data were obtained from a study by Cahill (2006); the collection of the data was funded by the National Institute of Justice (NIJ) and is available through the Inter-university Consortium for Political and Social Research (ICPSR). These data contain the block group average property crime from 1998 to 2002 for three cities: Nashville, Portland and Tucson. Since, to our knowledge, these are the only data available on such a small scale, we chose these cities and this time period for our analysis. Our dependent variable is the average property crime rate per hundred households, and property crime is defined as burglary, larceny or motor vehicle theft without the use or threat of force.

Measures of income and socio-economic variables come from the 2000 Census.² Using GIS, we map Census income data to construct additional measures of income inequality. Figure 1 provides a map of block groups from Portland with property crime and median household income data. All three cities are of similar size and this single map is included as a representative example to visualise median incomes, crime rates and sizes of block groups in our sample. The data set contains 1292 observations at the block group level.

Figure 1.

Sample of Portland block groups, household median incomes and property crime rate per 100 households.

The main variables of interest are the measures of income inequality within and across block groups. The within-block group income measurements are the percentage of households under the poverty line of US$20,000, the percentage of households over US$75,000, and the Gini coefficient. We include the Gini coefficient in our study as it is the most commonly used measure of income inequality. However, Wilkinson and Pickett (2006) and this study raise concerns over using the Gini coefficient at local levels where there are very few observations. In our data set, the mean number of households per block group is 523, which is quite small, with a standard deviation of 365. Given the small number of households, we further explore the nature of the Gini coefficient at such a small scale.

A low Gini coefficient indicates similar incomes within a group, while a high Gini coefficient indicates unequal incomes within a group. At the block group level, we expect to observe clusters of both high and low incomes that result in a low Gini coefficient. However, this is not the case. The data indicate there are block groups with clusters of rich households and a low Gini coefficient, but very few block groups with a high percentage of poor households and a low Gini coefficient. Figure 2 illustrates the strong positive correlation (0.6786) between the Gini coefficient and the percentage of households under the poverty level. Figure 3 illustrates a weak negative correlation (−0.2838) between the Gini coefficient and the percentage of households with incomes greater than US$75,000. These data suggest a higher Gini coefficient picks up an increase in the number of poor households within a block group. There are a couple possible explanations for this pattern. First, extremely high household income values are capped at US$200,000 as the Census does not categorise incomes above this amount. In this way, it is not possible for very few extremely large household incomes to generate a high Gini coefficient. Second, each block contains a relatively small number of households (mean of 523), and so it is possible that block groups can have varying income distributions. For example, 6.3% of block groups have an income range from US$ 0 to US$75,000, while 40.5% of block groups have an income range that is the widest possible, US$ 0 to US$200,000. Additionally, there are over 50% of block groups which have the high end of their range between US$75,000 and US$200,000. The varying ranges of income amongst the block groups can lead to Gini coefficient values that indicate very little about true inequality. In blocks groups with a narrow range (US$ 0 to US$75,000) we observe a high poverty concentration and a few households at the high end of the block group’s income range. This combination leads to a high Gini coefficient, even though the majority of the households have relatively low incomes. For example, in one block group, 70% of households earn less than US$20,000 and no household earns more than US$75,000, but their Gini coefficient is quite high, 0.51, because 13% of households earn between US$50,000 and US$75,000.

Figure 2.

Percent of low-income households versus Gini.

Figure 3.

Percent of high income households versus Gini.

As previously discussed, the Gini coefficient cannot measure the level of inequality across observations. Thus, we construct income inequality measures that allow for comparisons of median income across neighbouring block groups. The first measure, Richer than Neighbours, is a dummy variable equal to 1 if one’s own block group median income is greater than all neighbouring block group median incomes. The next measure, Poorer than Neighbours, is a dummy variable equal to 1 if one’s own block group median income is less than all neighbouring block group median incomes. These variables capture differences in the relative income of neighbourhoods which may drive criminal behaviour.

Roughly 75% of all block groups are neither the richest nor the poorest relative to their neighbouring block groups. With these block groups in mind, we created measures to indicate the size of the income gap between one’s own block group and the poorest and richest neighbouring block group. The following equations refer to block group level variables.

\begin{array}{l} % Inc Difference from Richest Neighbor \\ = \frac{(M e d i a n H o u s e I n c - M a x N e i g h b o r M e d i a n I n c)}{M e d i a n H o u s e I n c} * 100 % \end{array}

(1)

\begin{array}{l} % Inc Difference from Poorest Neighbor \\ = \frac{(M e d i a n H o u s e I n c - M i n N e i g h b o r M e d i a n I n c)}{M e d i a n H o u s e I n c} * 100 % \end{array}

(2)

It is worth noting that each block group, even if it is the richest (or poorest) as indicated by the dummy measure, has a non-zero percentage income difference from their richest (or poorest) neighbour. For example, if a block group is the richest among its neighbours (Richer than Neighbours dummy equal to 1), then their percentage income difference is the gap between their income and the second richest block group which they neighbour.

Several control variables associated with crime levels were included in the analysis as well. These variables include population density, education, unemployment, vacant housing, distance to the Central Business District (CBD) and income. Population density controls for number of potential burglars and victims, which is defined as the number of people per square kilometre. The percentage of people with high school and college degrees indicate the level of education. We expect more educated areas to have less crime (Lochner and Moretti, 2004). The controls for the percentage of unemployment and vacant housing variables indicate the economic wellbeing of an area. Distance to the CBD is used to control for the number of presented crime opportunities as it may be more or less populated with visitors during certain times of the day than residential areas (Bernasco and Luykx, 2003). A description of each variable and summary statistics are provided in Table 1.

Table 1.

Descriptive statistics.

Variable	Description	Mean	Standard deviation	Minimum	Maximum
Property Crime	Average property crime rate per 100 household, 1998–2002	19.87	24.87	0.02	296.8
Population Density	Population density per square kilometre, 2000	200.54	134.76	0.46	1112.67
Unemployment	% unemployed, 2000	4.04	3.34	0	43.13
College Grad	% over the age of 25 with college degree, 2000	33.85	20.05	0	96.15
Only HS Grad	% over the age of 25 with high school degree only, 2000	23.63	9.70	0	48.20
Vacant Housing	% of vacant housing units, 2000	6.47	4.91	0	53.60
Distance to CBD	Distance to downtown in miles, 2000	4.13	2.97	0.01	16.00
Poverty	% of households with less than US$20,000 income, 2000	25.84	16.23	0.72	94.99
High Income	% of households with more than US$75,000 income, 2000	16.47	14.57	0	76.76
Gini	Block group income Gini coefficient, 2000	0.38	0.06	0.21	0.62
Richer than Neighbours	Equal to 1, if block group median income is greater than neighbouring median incomes, 2000	0.12	0.33	0	1.00
Poorer than Neighbours	Equal to 1, if block group median income is less than neighbouring median incomes, 2000	0.12	0.33	0	1.00
% Income Difference from Richest Neighbour	See eq. (1)	−55.95	78.81	−773.18	60.56
% Income Difference from Poorest Neighbour	See eq. (2)	28.74	28.81	−186.93	87.80

Methodology

The goal of our analysis is to determine the relationship between income inequality and crime. As a benchmark, we use OLS regression to estimate the coefficients of a semi-log function representing the relationship between property crime and income inequality, controlling for socio-economic characteristics. We estimate the following function:

\ln P C_{ic} = α X_{ic} + β Y_{ic} + γ Z_{ic} + δ_{c} + ε_{ic}

(3)

where $P C_{ic}$ is the property crime rate in Census block group i, in city c. $X_{ic}$ is a vector of socio-economic variables within a block group. $Y_{ic}$ is a vector of income inequality measures within a block group. $Z_{ic}$ is a vector of income inequality measures across neighbouring block groups. $δ_{c}$ is a city dummy variable.

The OLS estimates provide a benchmark for interpretation but are likely to be biased. The OLS model assumes independence among observations which most likely does not hold for our small-scale crime data since high crime rates tend to cluster together. Unobservable characteristics are also likely to be spatially correlated (Mears and Bhati, 2006; Morenoff et al., 2001). For example, the level of police protection, which is not observed in our model, is likely to have spillover effects into surrounding areas.

To account for spatial autocorrelation in the data we employ a Cliff-Ord spatial autoregressive model with spatial autoregressive disturbances.³ We estimate the following function:

lnP C_{ic} = λ WlnP C_{ic} + α X_{ic} + β Y_{ic} + γ Z_{ic} + δ_{c} + u_{ic}

(4)

u_{ic} = ρ W u_{ic} + ε_{ic}

(5)

where W is a spatial weight matrix, $λ$ and ρ are spatial autoregressive coefficients which indicate the strength of spatial autocorrelation in property crime and the error term, respectively. The spatial weight matrix accounts for the spatial dependency of crime rates across block groups. We use a spatial contiguity matrix with queen criteria which indicates whether block groups share a boundary. The elements of the spatial weight matrix have values of one if the block groups share a boundary and zero otherwise.^4,5

One important final issue to note is that the dependent variable is a 5-year average of property crime from 1998 to 2002 while the key income variables are from the 2000 Census. This data issue is concerning from a timing stand point as income and demographic variables from a single year are used to explain average crime rates. Averaged crime data makes it difficult to accurately uncover the relationship between crime and socio-economic variables (Andresen, 2006). However, we note that this is common practice in the literature, see Krivo and Peterson (1996) and He et al. (2015) for a review. While several studies use single year crime and Census data to avoid this timing issue, most are at larger geographic scales (i.e. cities) in which timing is quite important to the relationship (Bjerk, 2010). He et al. (2015) examined the timing issue at a small scale and while they find that the averaging crime data may be unnecessary in most situations, they do not conclude it to be inferior in all instances.

Results

Our initial analysis uses the OLS model from equation (3) and only contains income inequality measures within a block group which allows us to investigate the performance of the Gini coefficient. The results are presented in Table 2. We withhold the discussion of the control variables from Table 2 to focus on the Gini coefficient. We present five specifications to investigate how income level (measured by % Poverty and % High Income) and the Gini coefficient perform. In all specifications, the coefficients for % Poverty and % High Income are significant. Lower incomes are associated with more property crime and higher incomes with less.

Table 2.

Income inequality within-block group.

	(1)	(2)	(3)	(4)	(5)
Population Density	−0.0013***	−0.0012***	−0.0009***	−0.0011***	−0.0005**
	[0.0002]	[0.0002]	[0.0002]	[0.0002]	[0.0002]
Unemployment	0.0327***	0.0328***	0.0355***	0.0363***	0.0454***
	[0.0071]	[0.0078]	[0.0073]	[0.0069]	[0.0072]
College Grad	−0.0030	−0.0030	−0.0088***	−0.0037*	−0.0123***
	[0.0021]	[0.0022]	[0.0019]	[0.0020]	[0.0018]
Only HS Grad	−0.0077**	−0.0077*	−0.0035	−0.0086**	−0.0045
	[0.0038]	[0.0041]	[0.0038]	[0.0038]	[0.0039]
Vacant Housing	−0.0179*	−0.0179***	−0.0160	−0.0161	−0.0109
	[0.0104]	[0.0051]	[0.0107]	[0.0104]	[0.0108]
Distance to CBD	−0.0574***	−0.0573***	−0.0609***	−0.0623***	−0.0751***
	[0.0108]	[0.0093]	[0.0110]	[0.0108]	[0.0112]
Poverty	0.0069***	0.0065**	0.0148***
	[0.0022]	[0.0028]	[0.0032]
High Income	−0.0215***	−0.0215***		−0.0238***
	[0.0032]	[0.0027]		[0.0031]
Gini		0.1259	−0.3440	0.8781**	1.4991***
		[0.5330]	[0.6353]	[0.4274]	[0.4462]
Observations	1,292	1,292	1,292	1,292	1,292

Adjusted R-squared	0.241	0.241	0.203	0.238	0.185

Notes: Results from estimating OLS model with city dummies where the dependent variable is the natural log of property crime rate per 100 households. Robust standard errors displayed in brackets. *** indicates significance at 1% level, ** indicates significance at 5% level, * indicates significance at 10% level.

The results for the Gini coefficient indicate that it may not explain property crime within a block group. Columns 1 and 2 from Table 2 include % Poverty and % High Income, additionally column 2 includes the Gini coefficient. An examination of these two specifications indicates that the Gini coefficient does not explain differences in property crime when absolute levels of income measurement are present. The coefficient on the Gini is insignificant in column 2 and the R-squared does not change from column 1 to 2. This result is not too surprising since the percentage of poor and rich already represent the level of inequality within a block group. However, columns 4 and 5 drop % Poverty and the coefficient on the Gini is positive and significant. This result indicates that higher levels of income inequality as represented by the Gini coefficient correspond to higher property crime rates. As previously mentioned in the discussion of the Gini coefficient, % Poverty is positively correlated with the Gini coefficient. It is very likely the Gini coefficient is picking up the amount of poor households rather than the true inequality in the block group. When % Poverty is excluded the Gini coefficient shows a positive significant relationship with the property crime rate. The result in column 3 confirms this hypothesis. When % Poverty is included in the specification, its coefficient is positive and significant while the Gini coefficient is insignificant. The mixed results for the Gini coefficient in Table 2 may explain peculiar results from previous research on the relationship between income inequality and property crime at small geographic areas. Moreover, as previously noted, Census income data are only collected from 1/6 of households in a block group, which in our sample is approximately 87 households on average. For this reason, the calculated Gini coefficient is likely to have a large standard error, making it an unreliable measure of income inequality, which may have led to the results in Table 2. Given the lack of explanatory power and the unreliability of the Gini coefficient, we choose to omit it from the remaining regressions and instead focus on the effect of income inequality across block groups.⁶

Table 3 contains results for the coefficients of greatest interest, income inequality measures across block groups. The results in column 1 indicate Poorer than Neighbours, that is the poorest block group, compared with its neighbours, has a significantly lower property crime rate that is roughly 50.3% lower. This result is not a surprise; richer neighbourhoods have little incentive to steal from the poor. Holding all else constant, if nearby neighbourhoods are relatively richer and have more valuable items than one’s own neighbourhood, then one can expect their own neighbourhood to have relatively less property crime.

Table 3.

Income inequality within and across block group.

	(1)	(2)	(3)	(4)
Population Density	−0.0012***	−0.0014***	−0.0011***	−0.0013***
	[0.0002]	[0.0002]	[0.0002]	[0.0002]
Unemployment	0.0308***	0.0217***	0.0277***	0.0194***
	[0.0074]	[0.0071]	[0.0073]	[0.0074]
College Grad	−0.0028	−0.0007	−0.0032	−0.0012
	[0.0021]	[0.0020]	[0.0020]	[0.0019]
Only HS Grad	−0.0083**	−0.0058	−0.0082**	−0.0057
	[0.0037]	[0.0036]	[0.0037]	[0.0035]
Vacant Housing	−0.0180*	−0.0177**	−0.0218**	−0.0201**
	[0.0100]	[0.0087]	[0.0101]	[0.0089]
Distance to CBD	−0.0453***	−0.0244**	−0.0328***	−0.0173*
	[0.0098]	[0.0095]	[0.0108]	[0.0101]
Poverty	0.0118***	0.0074***	0.0137***	0.0074***
	[0.0023]	[0.0023]	[0.0026]	[0.0025]
High Income	−0.0215***	−0.0146***	−0.0226***	−0.0161***
	[0.0031]	[0.0030]	[0.0031]	[0.0030]
Richer than Neighbours	0.0956	−0.0142
	[0.0696]	[0.0623]
Poorer than Neighbours	−0.5024***	−0.3781***
	[0.1074]	[0.0978]
% Income Difference from Richest Neighbour			0.0005	−0.0001
			[0.0004]	[0.0004]
% Income Difference from Poorest Neighbour			0.0071***	0.0053***
			[0.0012]	[0.0010]
Ln Median Neighbour Property Crime Rate		0.5854***		0.5660***
		[0.0858]		[0.0816]
Observations	1292	1292	1292	1292
Adjusted R-squared	0.268	0.363	0.281	0.368

The coefficient on % Income Difference from Poorest Neighbour in column 3 indicates that a 1% increase in the income gap leads to a 0.72% increase in the property crime rate. This positive and significant effect suggests that a larger positive income gap creates an incentive for the residents in the poorer neighbourhoods to steal from the richer neighbourhoods, leading to increased property crime rates. This result matches the theory laid out by Chiu and Madden (1998).

On the other hand, income inequality measures dealing with the richest neighbourhood indicate no relationship with property crime. The results in columns 1 and 2 indicate Richer than Neighbours, that is the richest block group, compared with its neighbours, has no significant difference in property crime. This result is contrary to what one may expect. For example, if a block group has a higher income than its neighbours, then the poorer neighbours would have an incentive to steal from the richest block group. Thus, one would expect a positive coefficient for the Richer than Neighbours dummy. Our results do not support this claim. It is likely the richest neighbourhood knows the poor have an incentive to steal from them and so they increase security measures to protect against property crime. This action by the rich is very likely to produce the lack of a result seen here.

The lack of a result for the Richer than Neighbours dummy variable along with the result for % Income Difference from Poorest Neighbour may appear to be contradictory, but these two measures capture different aspects of income inequality. The lack of a result indicates that the richest area does not experience more crime than all surrounding areas. This result can be reconciled with the result from the percentage difference from the poorest area. As a single area becomes richer than the poorest, it tends to have more crime, but the richest area does not experience an increase crime beyond the gap effect with the poorest area.

With respect to % Income Difference from Richest Neighbour, columns 3 and 4 indicate that a change in the income gap does not lead to a significant difference in property crime. This result indicates that as the income gap between one’s own block group and the richest neighbour becomes smaller, there is no change in the level of property crime for one’s own block group. This result is contrary to what one may have expected. For example, a block group whose income is increasing towards the richest neighbour could attract more property crime as there are more valuable items to steal. Similarly, a positive coefficient could result from a block group whose income is decreasing away from the richest neighbour, leading to less property crime as there are fewer valuable items to steal. The lack of a result for this coefficient indicates that inequality measures with the richest neighbour are not relevant. The income relationship with the richest neighbour does not alter the motive or opportunity to commit property crime in one’s own block group.

For the key control variables, all columns in Table 3 indicate an increase in unemployment and poverty lead to statistically significant increases in the property crime rate. Also, increases in population density, vacant housing and distance to the CBD lead to statistically significant decreases in the property crime rate. These results are in line with previous research.⁷ While multicollinearity of the independent variables is a concern, the variance inflation factor (VIF) values for the regressions in Table 3 indicate multicollinearity is not problematic.⁸

Since high crime rates are likely to be clustered at the block group level, OLS estimates could be biased. In an effort to motivate the use of spatial modelling in this context, we included the median property crime rate for neighbouring block groups in the OLS model. Columns 2 and 4 of Table 3 present the results. The coefficient for median neighbouring property crime rate is positive and significant. This indicates property crime tends to spillover. As property crime in neighbouring areas increases so does property crime in one’s own block group. This result along with a positive Moran’s I for property crime and the residual indicate the use of a spatial model is appropriate for the data.

To correct for the biased results from the OLS estimation, we estimate the SARAR model specified in equations 4 and 5. Columns 1 and 2 in Table 4 present results from a spatial autoregressive model (SAR) in which only global spatial autocorrelation is assumed to exist. Columns 3 and 4 present results from a spatial error model (SEM) in which only spatial autocorrelation of residuals is assumed to exist. Columns 5 and 6 present the results for the SARAR model. From a theoretical perspective we prefer the SARAR model as it accounts for spatial autocorrelation in both crime and unobservables, but we include the two other models to determine if our main results are robust to different spatial modelling choices. For all three models our key results do not change. The coefficients are significant, of the same sign and similar magnitude as the previous OLS model.

Table 4.

Spatial model.

	SAR		SEM		SARAR
	(1)	(2)	(3)	(4)	(5)	(6)
Population Density	−0.0013***	−0.0012***	−0.0014***	−0.0013***	−0.0014***	−0.0013***
	[0.0002]	[0.0002]	[0.0002]	[0.0002]	[0.0002]	[0.0002]
Unemployment	0.0299***	0.0270***	0.0284***	0.0259***	0.0285***	0.0260***
	[0.0075]	[0.0075]	[0.0074]	[0.0074]	[0.0074]	[0.0074]
College Grad	−0.0023	−0.0028	−0.0039*	−0.0041*	−0.0037*	−0.0040*
	[0.0021]	[0.0021]	[0.0022]	[0.0022]	[0.0022]	[0.0022]
Only HS Grad	−0.0075*	−0.0074*	−0.0069*	−0.0070*	−0.0068*	−0.0069*
	[0.0040]	[0.0039]	[0.0039]	[0.0039]	[0.0039]	[0.0039]
Vacant Housing	−0.0185***	−0.0221***	−0.0157***	−0.0192***	−0.0160***	−0.0195***
	[0.0049]	[0.0049]	[0.0050]	[0.0050]	[0.0050]	[0.0050]
Distance to CBD	−0.0421***	−0.0307***	−0.0518***	−0.0400***	−0.0509***	−0.0393***
	[0.0092]	[0.0094]	[0.0107]	[0.0109]	[0.0107]	[0.0108]
Poverty	0.0113***	0.0131***	0.0099***	0.0121***	0.0100***	0.0121***
	[0.0023]	[0.0026]	[0.0023]	[0.0027]	[0.0023]	[0.0027]
High Income	−0.0204***	−0.0216***	−0.0192***	−0.0206***	−0.0192***	−0.0206***
	[0.0026]	[0.0026]	[0.0027]	[0.0026]	[0.0027]	[0.0026]
Richer than Neighbours	0.0788		0.0729		0.0714
	[0.0718]		[0.0700]		[0.0702]
Poorer than Neighbours	−0.4895***		−0.4419***		−0.4453***
	[0.0736]		[0.0716]		[0.0719]
% Income Difference		0.0004		0.0005		0.0005
from Richest Neighbour		[0.0004]		[0.0004]		[0.0004]
% Income Difference		0.0068***		0.0062***		0.0063***
from Poorest Neighbour		[0.0009]		[0.0009]		[0.0009]
Lambda (Crime)	0.0179***	0.0164***			0.0039	0.0033
	[0.0036]	[0.0036]			[0.0045]	[0.0045]
Rho (Error)			0.0524***	0.0496***	0.0486***	0.0463***
			[0.0067]	[0.0068]	[0.0082]	[0.0082]
Observations	1292	1292	1292	1292	1292	1292

Notes: Results from estimating maximum likelihood spatial models with city dummies where the dependent variable is the natural log of property crime rate per 100 households. Standard errors displayed in brackets. *** indicates significance at 1% level, ** indicates significance at 5% level, * indicates significance at 10% level.

In order to interpret the results from the spatial model we calculate marginal effects as the coefficients in Table 4 are not directly interpretable. The following are the marginal effects for the three significant income variables in column 6 for the SARAR model. The average total impact of a 1% increase in the percentage of households under the poverty line is estimated to have a 0.48% increase in the block group property crime rate. The average total impact of a 1% increase in the percentage of high income households is estimated to have a 0.81% decrease in the block group property crime rate. The average total impact of a 1% increase in the income difference from the poorest neighbouring block group is estimated to have a 0.25% increase in the block group property crime rate. These marginal effects are of similar magnitude as in the previous OLS model.

Conclusion

This paper indicates that income differences within and across block groups explain property crime variation in urban areas. To our knowledge, this is the only paper which studies the spatial structure of income inequality and property crime at the block group level. Property crime rates differ substantially at the block group level, and the spatial analysis of income data at this level provides insight into these differences. The only study which approaches the block group scale is a study by Whitworth (2013), which has a small geographic scale for crime, but uses an increasing geographic scale to measure income inequality within an area (up to 15–20 km in size). Our study improves on Whitworth (2013) and other income inequality and property crime studies by measuring inequality across geographic areas and not merely within an area. Unlike Whitworth (2013), we find income inequality affects property crime rates on the micro level. This improvement is most likely due to our deviation from the Gini coefficient and the use of new measures which capture inequality across areas.

An interesting result from our analysis is that the relatively poorest block group has less property crime than their neighbours. This may indicate the poorest area has less valuable property which relatively richer neighbours have little desire to steal. We further find that the relatively richest block group in an area experiences no change in property crime because of their higher income. This lack of a result may indicate that the richest neighbourhood increases their level of security, which reduces the opportunity for the poor to steal from the rich. Results also indicate that as one’s own area becomes relatively richer compared with the poorest neighbour, then property crime increases in one’s own neighbourhood. This result supports the general belief that as income inequality increases, property crime increases and gives specific support to Chiu and Madden (1998) theory on property crime and income inequality between rich and poor neighbourhoods. Previous literature has shown mixed results for income inequality and property crime. The methodology in this paper allows for an improved measurement and analysis of this relationship across geographic areas which may have led to the results.

We must caution readers on the robustness of these results to other cities. Block groups can vary dramatically in size across different cities. These size differences as indicated by the MAUP may mask the true relationship between variables or lead to the finding of a result when one truly does not exist. Possible avenues for future research could investigate the geographic scale and sample size at which the Gini coefficient is an appropriate measure of within group income inequality. Additionally, one may want to investigate how the methodology used in this paper holds up as the geographic scale increases in size.

Footnotes

Appendix

Spatial model (inverse distance weighting matrix).

	SARAR
	(1)	(2)
Population Density	−0.0018***	−0.0013***
	[0.0002]	[0.0002]
Unemployment	0.0253***	0.0257***
	[0.0070]	[0.0073]
College Grad	−0.0033	−0.0021
	[0.0026]	[0.0023]
Only HS Grad	−0.0045	−0.0063
	[0.0040]	[0.0040]
Vacant Housing	−0.0151***	−0.0205***
	[0.0049]	[0.0049]
Distance to CBD	−0.1171***	−0.0379***
	[0.0196]	[0.0119]
Poverty	0.0072***	0.0116***
	[0.0024]	[0.0027]
High Income	−0.0177***	−0.0209***
	[0.0027]	[0.0026]
Richer than Neighbours	0.0626
	[0.0676]
Poorer than Neighbours	−0.3678***
	[0.0691]
% Income Difference from Richest Neighbour		0.0004
		[0.0004]
% Income Difference from Poorest Neighbour		0.0061***
		[0.0009]
Lambda (crime)	−0.2771	0.7641***
	[0.3667]	[0.1230]
Rho (error)	3.2252***	0.8609***
	[0.0944]	[0.0972]
Observations	1292	1292

Funding

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

Notes

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