On the Correlation Between Crime and Punishment

In two previous posts (here and here) I've taken a look at the OECD's 50^th anniversary present to all of us - their "Better Life Index" (BLI). One of the eleven components of that Index is titled "Safety" - and according to the OECD this component

"...... largely reflects the risks of people being physically assaulted or falling victim to other types of crime. Crime may lead to loss of life and property, as well as physical pain, post-traumatic stress and anxiety. The biggest impact of crime on people’s well-being appears to be through the feeling of vulnerability that it causes."

The BLI site also notes that

"Across the OECD, one person in six reported falling victim to a conventional crime, with physical assault accounting for nearly a quarter of all conventional crime. In terms of perceived safety, one out of four people in the OECD report feeling unsafe on the street after dark."

In addition, the average homicide rate across the OECD countries is 2.2 murders per 100,000 inhabitants.

An interesting question that arises is whether or not the relative safety level matches the relative incarceration rate.

The word "relative", here, is with respect to other OECD countries. Data for the incarceration rate (prisoners per 100,000 population) in different countries are gathered by the International Centre for Prison Studies in the United Kingdom, and are summarized on Wikipedia. The numbers for the OECD countries, together with those for the overall BLI (and its Safety component), are given below, and are also available in an Excel workbook on the Data page of this blog. Two versions of the full BLI are given - one that gives equal weighting to each of the 11 components, and one that uses "optimal" weights based on the Principal Components analysis in one of my earlier posts.

                           Incarceration                 BLI        BLI        BLI
                                 Rate                     (equal)    (opt.)      Safety

Australia	133	8.100	8.7	9.2
Austria	103	7.064	7.3	9.1
Belgium	97	6.882	7.2	7.0
Canada	117	8.091	8.4	9.2
Chile	312	3.800	3.7	3.4
Czech Republic	207	5.855	6.3	8.3
Denmark	71	7.727	8.2	8.4
Estonia	256	4.127	4.5	5.4
Finland	60	7.455	7.8	8.5
France	96	6.845	7.2	8.0
Germany	88	6.936	7.2	8.8
Greece	102	5.255	5.4	8.6
Hungary	153	4.664	5.2	8.4
Iceland	55	7.391	8.0	9.5
Ireland	99	7.064	7.6	8.6
Israel	325	6.018	6.0	8.3
Italy	113	5.682	5.8	8.2
Japan	62	6.064	6.3	9.7
Korea	98	5.291	5.3	8.7
Luxembourg	139	7.436	7.4	8.2
Mexico	200	3.655	4.1	0.0
Netherlands	94	7.455	7.6	8.2
New Zealand	203	7.900	8.7	9.1
Norway	71	7.818	8.1	9.0
Poland	214	5.327	5.7	9.1
Portugal	109	4.609	5.0	7.6
Slovak Republic	185	4.964	5.5	8.4
Slovenia	67	5.945	6.3	8.8
Spain	59	5.882	6.4	8.5
Sweden	78	8.009	8.5	8.1
Switzerland	79	7.527	7.5	8.6
Turkey	164	2.736	2.8	7.0
Great Britain	150	7.245	7.7	8.6
USA	743	7.555	7.7	7.6

Now, let's take a look at Spearman's rank correlation between the incarceration rate and the BLI. We need to keep in mind that with respect to the latter, large values mean better.


Incarceration Rate  and:            BLI                BLI                BLI
                                            (equal wts.)      (opt. wts.)       Safety     

                                                -0.354             -0.383            -0.386
                                               [0.040]             [0.026]           [0.024]

Using Kendall's tau statistic, the same picture emerges:

                                               -0.240             -0.254            -0.275
                                              [0.049]             [0.038]           [0.026]

In each case, the figures in square brackets are p-values for the test of the hypothesis that the rank correlation is zero, against a 2-sided alternative. (Just halve them if you have a prior about the sign of the correlation.)

There's a significant negative rank correlation between the incarceration rate and the BLI, as a whole, or just for the Safety component of that index. In other words, in terms of country rankings, high incarceration rates tend to be associated with low levels of safety and "Quality of Life".

Possibly, this means that the police and the courts are doing their job well. But we'd have to look at the crimes for which folk are being jailed, and line these up against the the details behind the Safety component of the BLI.

Or maybe it suggests that prisons detract from our well-being because they're a blot on the landscape! I don't know.

However, for a discussion of a possible connection between on the incarceration rate and a country's stand on drug usage, see the recent post on the Carpe Diem blog.

© 2011, David E. Giles