Notes on Crime Trends in the US

Notes on Crime Trends in the US

I was recently quoted in a NOTUS article about crime trends in the US—specifically, that crime has been trending downward across all crime types, even during the Biden administration.

Here is the graph I used to make that determination.

If you want to skip to the end, you can see the technical report I wrote on how I calculated those smooth trends (via the sample of cities in Jeff Asher’s Real Time Crime Index).

National politics, in my opinion, tend to have little to nothing to do with local crime trends. But there are definitely national crime trends. Here are my notes for others to follow along, as well as a description of statistical models to estimate those national trends and identify local deviations from those trends.

Cities Share a Common US Trend

When I used to teach, I shared this graph with students to illustrate that there were shared national trends. The following graph shows homicide trends over time in Dallas, New York City, and Chicago:

Although the three cities are far apart, you can clearly see that they followed similar patterns: an increase from the 1960s to the early 1990s, potentially with a flat period from the mid-1970s through the 1980s, followed by a crime decline beginning in the early 1990s. The cities may shift the pattern by a few years and show level shifts up or down (Dallas has always been higher than New York City), but they generally follow similar trends over time. This pattern was shared across many cities, not just these three.

The cities can simultaneously have bumps, like Chicago did in 2016. We will want to model that national trend, but also allow the model to vary enough to identify those level differences between cities, as well as bumps when they diverge from those overall trends.

Breaking Down into Trend and Season with Subannual Data

When looking at crime data at subannual intervals, you can often see regular ups and downs. A convenient way to analyze a time series with regular seasonal patterns is to separate it into seasonal, trend, and residual components.

Here is an example of burglaries in the US, based on the sample of agencies collected by the Real Time Crime Index (RTCI). The first panel shows the actual observed counts1, and the panels below show statistical estimates of the overall trend, the regular seasonal component, and the residual.

So this shows a fairly smooth decline over time after filtering out the seasonal component. This is for the cumulative burglary data (from the RTCI), but I fit a model that basically estimates this for every city in the RTCI. I do not want to get too much into the technical details, but I fit a random effects logistic regression model for the rates, so it takes into account that some cities’ rates are more volatile due to smaller population counts. Again, all code to replicate the graphs is on GitHub.

The trend and seasonal components are calculated via splines and multiple Fourier terms, respectively. I then have global terms for these (which characterize the entire US) and city terms (so you can look at deviations from the average). In the logit model, you can explicitly model the residual term, so you can get a standard error for the residual effect.

Here I am going to walk through one city estimate, Philadelphia, as an example. Here are Philadelphia’s observed data (light gray), fitted trend and season (orange line), and the US average trend and season (blue line). They appear in sync in both trend and season, although Philadelphia has an upward level shift. You can also see some spikes in Philadelphia’s observed data relative to the smoothed data.

The next figure shows the STL-type chart but compares the trend and seasonal components in a way that makes their scales similar, making changes in the shapes of the curves easier to see while ignoring the level shift.

This lets you compare the global trend, seasonal, and residual components (blue) with Philadelphia’s estimated components. For the trend and seasonal components, I plot Philadelphia’s estimates with standard errors, making it easier to identify significant differences by eye. Philadelphia’s long-term trend is somewhat flatter than the national decline in burglary rates. Its seasonal component is very similar to the national pattern.

In the residual chart, you can see a large spike in 2020 (which happened to correspond to a few extra hundred commercial burglaries related to the George Floyd protests).

While the report just has this example for Philadelphia, I have a web app you can filter for individual cities and get these same graphs and stats for any city of interest.

Looking at Deviations from National

Via the model, I can look at the trends or seasonal components that vary from the national curve. Here is a graph of violent crime trends:

This identifies Baltimore’s violent crime trend as declining more than the US trend would suggest, consistent with several of...