Introduction

The topic of violence, specifically involving firearms, peaked my attention lately as there seems to be an alarming amount of attacks in Toronto. In order to see whether my hunch was right, I looked through some publicly available data to performed some exploration. Primarily using data from Statistics Canada and the Toronto Police Service. My analysis is more focused on Toronto, since that's where I'm based in.

The first question I want to answer is to see whether there is an increase in crime. While it sounds simple, there were three dimensions to consider.

Types of crime (homicide by shooting, injuries by shooting, firearm discharge, firearm pointing, or use of firearm).

Timespan (Past 5, 10, or 20 years) and frequency (annual or monthly)

Geographic Location (national, provincial, municipal, or city)

The second question I want to look at is whether there is a relationship with other statistics in Toronto with these (potential) increase in crime levels. Some preliminary research shows factors such as income level, population density and education level to be some primary influencers of crime. With the new cannabis regulation coming in, I also wonder if expected drug trade flow change has any effects.

Highlight of Results (or Abstract, or Executive Summary, or TL; DR)

Crime in general trended up significantly in the past four years in Toronto and Canada.

Past 2 decades, we had a significant decrease in police reported crime in Canada.

Firearm related crime has trended up in the past 10 years, specifically in the past four years in Toronto and Canada.

Predicted about 5% increase in firearm incidents in Toronto in 2018 compared to 2017

Forecasted 18% or 39% increase in shooting deaths in Toronto in 2018 compared to 2017, depending on the algorithm. The prediction range is -23% to 90% compared to 2017 numbers, using the 95% confidence interval.

The relationship isn't clear cut, but it seems like the increase in firearm deaths doesn't relate to headline economic factors. I suspect it's more likely to be policy related, such as legalization of cannabis or understaffing in Toronto Police Service. Though it's difficult to say for sure, as it is a very complex issue depending on many factors.

Has Firearm Related Crime Increased?

The simple conclusion is yes, firearm crime has increased. Firearm crime on an incident count basis, victim count basis, and firearm incidents as a percentage of population have all trended up for the last 10 years, though some trends are strong than others depending on which metrics you look at. There is also a stronger surge upwards around 2014 carrying into the present, showing a more dramatic increase in gun violence over the last three to four years. On the flip side, police reported crime in general was at the lowest level of 20 years in 2013 with a up trend in the past four years.

**Statistics** Canada's "Incident-based crime statistics, by detailed violations"

I made this simple dashboard showing annual crime data using a very comprehensive dataset from Statistics Canada called "Incident-based crime statistics, by detailed violations". Now let's look specifically into firearm crime.

Figure 1 below shows "Discharging Firearm with Intent" in Canada over time, showing total persons charged.

Figure 2 below shows "Discharging Firearm with Intent" in Toronto over time, showing total persons charged.

Toronto Police Service's Dashboard on Shootings

Looking at the Toronto Police Services Dashboard on Shootings here, I found significant up trends since 2014 as well.

Figure 4 below shows shootings in Toronto by year.

Figure 4 shows the occurrence and victims of shootings in Toronto. Note that 2016 and 2017 numbers are significantly higher than 2015, which is significantly higher than 2014.

Toronto has 262 count of shooting occurrence year to date as of August 19, 2018 and there are still 135 days left to the year. At an annualized rate (prorated by number of days), 2018 will have a forecasted 416 incidents of shootings, which is higher than previous years (5.3% higher than 2017).

To make sure this rough extrapolation based on the days is acceptable, I checked whether shootings across months are uniformly distributed. Based on monthly data in 2017 from the Toronto Police Service, it seems that the distribution across months for shootings is (very) roughly uniform. This prompts me to look into the seasonality of shootings so I can do a more accurate forecast which is in the later section of this post.

Figure 5 below shows monthly count of shootings in Toronto in 2017.

If we look at the number of deaths from shootings from figure 6, it breaks down number of victims by severity of injuries. At the time of the article, there are 32 deaths in 2018, which pro-rated to be 51 deaths in 2018, a 30.8% increase from 2017. Note that 2015~2017 has a much higher count of victims than 2014.

Figure 6 below shows number of victims and the injury severity in Toronto.

Just to make sure the data is not biased on population, I took a look at the incidents on a population adjusted basis (incidents per 100,000 residents), the results show similar trend since the population stayed relatively flat in Toronto and Canada.

Time Series Analysis

Using the Toronto Police data on shooting deaths per month (it had a few gaps that I had fill in using averages) from their "Public Safety Data Portal". I found some interesting patterns. This part is a bit more technical. Keep in mind, the data ends July 2018.

Figure 7 below shows the seasonal plots of deaths by shooting in Toronto.

There seems to be a pattern (particularly in July), so I use a decomposition to break it out. Results below.

Figure 8 below shows the decomposition of deaths by shooting.

The observed value (first row) shows the actual data, trend (second row) is the longer term trend with the seasonality and randomness taken out, seasonal (third row) is the recurring patterns and random (fourth row) is the "noise" in the data. We can see here that we are at the highest of a the seasonal pattern, so month over month, the rest of the year in 2018 we will likely see a decrease in monthly number of deaths by firearm.

Figure 9 below shows the autocorrelation and partial autocorrelation function.

Though there seems to be a a 12 month pattern, the autocorrelation is actually quite low with the ~0.15 bound. Autocorrelation is like normal correlation, but it looks at the correlation between the data point of current and previous periods. As an analogy, it's like saying today's weather will have the highest correlation with the weather yesterday. As well, yesterday's weather will have the highest correlation with the day before.

Forecast Model

Statistical models aren't complete if you don't make some predictions! I built a simple autoregression (12 period lag) model and a Holt Winters model.

Figure 10 below shows the forecast of next 5 months (August to December 2018) using the Autoregressive model.

Figure 11 below shows the forecast of next 5 months (August to December 2018) using a Holt Winters model.

Forecasts for Autoregressive Model (for the next 5 months) is 16, with a low of 0 and a high of 34 using the 95% confidence interval.

Forecast for Holt Winters (for the next 5 months) is 24, with a low of 4 and a high of 44 using the 95% confidence interval. Numbers are rounded of course.

Turning this to an annualized rates, we get 46 (AR) and 54 (HW) deaths in 2018. Which is 17.9% and 38.5% higher than 2017 # of deaths by firearm, respectively. The prediction range is -23% to 90% compared to 2017 numbers.

Discussion

I was slightly surprised by the results and how much more firearm related incidents there are in the previous three to four years compared to before. So the next steps to think about is "why". I took a quick look on theories and academic literature to look at long term patterns in crime.

Some Good News

From a Statistics Canada article in 2013, police reported crimes are in an overall decline over the past 2 decades and there are some theories suggesting why it is. “These factors include an aging population, changing policing practices and strategies, the rise of technology, shifts in unemployment, variations in alcohol consumption, neighbourhood characteristics, or changing attitudes towards illegal and risky behaviour.”

"Several factors commonly mentioned by experts as possible explanations for the decline in crime may be related primarily to certain types of crime. For example, multivariate analysis performed by the Canadian Centre for Justice Statistics indicated that changes in inflation tend to have the most association with changes in crime that is financially motivated (i.e., robbery, break and enter, motor vehicle theft), while changes in alcohol consumption and unemployment rates are correlated with changes in the homicide rate, and changes in the population's age and gender are associated with changes in the rate of break and enters."

This above quote is referring to this old(er), but really good, academic paper that analyzed long term patterns in crime by Statistics Canada called "Exploring Crime Patterns in Canada", written in 2005.

**Looking at Multivariate Effects of Social and Economic Variables**

Inflation

Inflation has a positive relationship to crime as it erodes low income individuals’ purchasing power. Inflation rate has overall been on the increase since our last recession and is currently being tackled by the Bank of Canada with increases in interest rate. The current headline inflation rate is 3.0% (YoY change July 2018), which is high for modern Canadian economy, but probably not high enough to have significant effect on crime. Though I can't say for sure, would need some heavier research to tell.

Unemployment Rate

The headline unemployment rate is extremely low at 5.8% for the July 2018 number (one of the lowest points in the past 40 years). From most literature, unemployment rate does have a positive relationship to crime. This is not so much in line with what's happening in Toronto where we have lower unemployment and higher crime.

Policy

Use of alcohol has a positive relationship with crime. With the new buck a beer initiative in Ontario, there may be an effect on crime. The legalization of cannabis is a bit of a tricky question. While it may decrease revenue of organized crimes, it may also prompt further competition and sales of other illegal drugs. There are a lot of discussions in this topic as cannabis becomes legalized towards the end of 2018. This article by Jerry Langton, who is the author of The Hard Way Out and The Secret Life of Bikers: Inside the Hidden World of Organized Crime put forwards some interesting thoughts.

Toronto Police Service

This may be related as well. The number of staff (uniform and civilian) is down in 2018 by 9.8% which is a (scary) large amount. This article elaborates on this a bit more.

This article from 2016 titled "Three theories that may explain Toronto’s gun violence spike" might be worth a read if you are interested in this specific topic.

Vector Autoregression

I decided to fit a VAR (vector autoregression model) to figure out what affects firearm deaths in Toronto. VAR is my favorite methods of looking at multivariate time series models and it's a pretty standard tool for economists.

I used monthly data from the Toronto Economic Bulletin from the Open Data Catalogue of Toronto. Link here. It includes various monthly industry sales in Toronto, as well as inflation, employment, EI usage...etc. Totaling 41 variables (including firearm crime). The data goes from January of 2004 to February of 2018, unfortunately I have to fill in a few gaps using averages, but overall, I'm really impressed with how complete the data is. Props to Toronto Economic Bulletin (though it took me a few hours to organize the data).

A vector autoregressive model takes in endogenous and exogenous variables. Simply put, endogenous variables are variables within a system and they affect each other. Whereas exogenous variables are external to the system and are independent but affects the endogenous variables.

For my endogenous variables, I used: firearm deaths, # of unemployed, part-time working rate, all item CPI, EI program usage, and monthly weekday TTC ridership. I'd look into which variables to put in as endogenous if I had time for further research.

Results from this is interesting. My multiple R squared is 71.77% and adjusted r squared is low at 11.36%, which is unsurprising. The p value of the f-stat is 25%. So overall, it isn't the best model, but for the first try, it came out surprisingly usable. The variables that has a significant relationship (at 10% confidence level) on firearm deaths are firearm deaths (lag 2, negative), monthly average TTC weekday ridership (lag 3, negative), CPI (lag 5, positive), part-time working rate (lag 7, negative), CPI (lag 7, positive), part time working rate (lag 8, positive), and finally, monthly average TTC weekday ridership (lage 12, positive).

The only consistent conclusion I can draw from this is that CPI has a statistically significant positive relationship with firearm deaths. The other variables, though significant, shows a bit of a mixed signal. If you are interested in learning more about factors that affect gun violence, I would encourage you to read up on some academic papers. Shoot me a email if you want to check out the data I used or if you want to chat about the model. The VAR I built was fairly preliminary since I'm not writing a full paper on this topic, but more just looking to see if there are any interesting patterns in Toronto's shooting data.

Some Opposing Views

While gun violence has gone up in the past 4 years or so, it's important to note that violence and crime in general has been decreasing for the past 2 decades as seen on the crime severity index from Statistics Canada. "The CSI measures both the volume and severity of crimes reported to the police." This article caution using statistics that makes crime looks worse than it actually is, so I went back and re-checked my article to make sure to give an objective view on the data.

Figure 12 below shows the crime severity index for the past 2 decades.

Final Thoughts

I tried to offer as many viewpoints as possible in this article and I hope it wasn't too overwhelming. All in all, the significant increase in crime over the past few years, specifically in firearm related crime is alarming to me. Though I don't think anyone can say for certain what is causing this. From my analysis, it doesn't seem to be a result of the current Economic condition, since the economy is doing great at the moment. It could be the new policies by the various levels of government, it could be a social/culture/attitude change, it could be changing structures in organized crime, the understaffing in Toronto Police, or it could be a change in economic structures (I'm thinking income inequality). There was a lot of other analysis I could have done (shootings to deaths by shoot ratio for instance), but I should probably get back to work.

What are your thoughts?

Special thanks to Kyla Litwiller who helped bounce some ideas and helped me with the edits.

Stay safe out there :)

Eric

Extra Resources

The Canadian Community Crime Tracker

This is a interesting resource I found that provides geographical data. It did not work in my Chrome browser, but worked in my internet explorer. See link here.

Toronto Crime App

Similar to the above, but focused on Toronto spatial crime data. See link here.