Common sense dictates that crime rates have an impact on house prices. It also dictates that it would be pointless to compare crime rates and property prices between, say, Leeds and Portsmouth. If you were looking for somewhere to live, you might narrow it down to a general area and then prefer a sub-area within that that had a lower crime rate. Theoretically this should lead to higher demand, hence higher prices in these lower crime sub areas

To measure the effect, I look at one square mile areas compared to the surrounding two square mile area. I then measure the percent difference in crime rate (the total number of crimes divided by the number of postcodes) and the difference in median prices between the inner and outer areas. Each point in the plot below represents a one square mile area in England:

As you can see, the lower the crime rate compared to surrounding areas, the higher the house price. The x-axis represents the difference in crime rates between a square and its surrounding square – 200 meaning that it has a 200% higher crime rate than surrounding areas. The median house price difference is plotted on the y-axis, where e.g., 150 means that the median house price in the square was 150% higher than the surrounding square.The fact that the graph slopes from left to right suggests that there is an inverse relationship between relative crime rates and house prices.

Estimate Std. Error t value Pr(>|t|) (Intercept) 11.550501 0.411319 28.08 <2e-16 *** Price Diff -0.153062 0.005883 -26.02 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 28.32 on 4904 degrees of freedom Multiple R-squared: 0.1213, Adjusted R-squared: 0.1211

So, for every percent increase in the difference in crime rate between an area and its surroundings, the median price drops by -0.16%. Furthermore, approximately 13% of the variability in house prices in an area with respect to its surrounding areas is explained by crime rates. I’ll explain what this means shortly.

The relationship is made clearer when the graph is taken at a log scale

### What areas of the UK are covered?

There are 3414 points in the graph above, covering 3414 sq miles of area in England, specifically the areas shown below:

The criteria for inclusion are having over 30 postcodes in the square mile and at least twice as many in the surrounding two square mile area, having at least 15 property sales between March and July 2018 and at least 15 reported crimes in the same period.The postcode criteria are meant to exclude any isolated one square mile areas that don’t have surrounding populated areas. Also excluded are places like Birmingham and Manchester city centres and Covent Garden in London that have a far higher postcode density than surrounding areas.

### How do the measurements work?

In the map below, the area being measured is in the inner square, while the area it is being compared to is outlined by the outer square. The inner square is 1×1 mile, while the outer area is 2×2 miles.

For the area above, these are what the numbers look like from September 2017 to August 2018:

Num Postcodes | Num Crimes | Crime Rate | Median Price | |

Inner Square | 293 | 2,684 | 9.1604 | 340,000 |

Surrounding Square | 2,594 | 7,208 | 2.7787 | 350,500 |

Diff % | 229.66% | -2.99% |

What this means is that the inner square has a 229% higher crime rate than the surrounding area and that house prices are 2.99% lower. The crime rate is calculated as the number of crimes divided by the number of postcodes in an area. I showed previously that there is a linear relationship between the number of postcodes and the number of crimes, so this will adjust for that.

### What about changes over time?

Another way to measure the impact on crime on house prices is to see if there is any correlation between a decrease/increase in crimes and house prices over time in the same square. To do this I took crime rates and prices between March and July of each of 2016, 2017 and 2018.

As opposed to the relationship between adjacent areas, there is no apparent relationship between change in crime vs change in price. The only interesting thing about this plot is that the majority of areas experienced a decline in crime over a two year period as shown by the clustering of points to the left of the zero-line for percentage change in crime.

### Outliers

Coming back to the original graph showing the increase in house prices as crime rates decline compared to surrounding areas, I want to look at some of the outliers (adjacent places that have the same crime rate but very different house prices and vice versa).

The first interesting outlier is Belgravia in London with a 160% higher price than its surrounding areas and 16.69% higher crime rate.

The more interesting outlier is this square mile near Runcorn with prices 215% higher and crime rate 54% higher as well.

Clearly there are factors other than crime rates that go into the desirability of certain areas.

So to put it simply, yes there is an effect of the relative rates of crime on price when you compare an area with its immediate surroundings. Maybe over a longer term a decline in crime rates does increase prices, but in the short term (one year) that effect is not visible.