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Prison population projectionsa cautionary perspective
Crime and justice statistics user dayMarch 2012
Sarah Armstrong (University of Glasgow)Elizabeth Fraser (Scottish Government Justice Analytical Services)
Scottish prison population - the history
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-01 2010-11
Scottish prison population - current drivers
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Total
Long term
Short term
Remand
Why do long term prison projections?
• Anticipate future need and plan development of prison estate
• Inform policy development - but this is only part of the story
How we do the projections• Sentenced receptions projected for adults and
young offenders • A range of time periods in order to account for
changes in trend over time• Time series analysis based on linear regression
and exponential smoothing• Six variants reflecting the overall trends over the
short (10 years), medium (25 years) and long (40 years) term: which best reflects the current situation?
• Need to compensate for inherent volatility over time, particularly for the smaller groups
Projections - special groups
• Remand receptions are particularly volatile and projected as proportion of direct sentenced receptions
• Recalls from licence projected as a proportion of the long-term population as It is very difficult to estimate how long such prisoners will remain in custody
Some issues
• Projections are based on assumptions about how the past relates to the future can be used for planning or cautionary tales
• If the future is uncertain, the one thing one can be sure of is that the projections will be wrong to some extent
• Sometimes the past may be misleading as well...
Long term projections (receptions)
Adults <6 m
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
Seasonal A1 short Linear A1 short
Seasonal A1 medium Linear A1 medium
Seasonal A1 long Linear A1 long
Adults 2y - 4y
0
200
400
600
800
1,000
1,200
1,400
1,600
1,800
Seasonal A4 short Linear A4 short
Seasonal A4 medium Linear A4 medium
Seasonal A4 long Linear A4 long
Adults 6m - 18m
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
Seasonal A2 short Linear A2 short
Seasonal A2 medium Linear A2 medium
Seasonal A2 long Linear A2 long
Adults 4y +
0
100
200
300
400
500
600
700
800
Seasonal A5 short Linear A5 short
Seasonal A5 medium Linear A5 medium
Seasonal A5 long Linear A5 long
Adults 18m - 2y
0
100
200
300
400
500
600
700
800
900
Seasonal A3 short Linear A3 short
Seasonal A3 medium Linear A3 medium
Seasonal A3 long Linear A3 long
Population projections to 2019-20
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
11,000
1982-83 1987-88 1992-93 1997-98 2002-03 2007-08 2012-13 2017-18
Ave
rage
dai
ly p
opul
atio
n
High
Historic data Low
Main
Accuracy of long term projections
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
Provisional estimate for 2011-12
Other population modelling
• Short term monthly projections– quick to produce, seasonally adjusted– still very volatile with large margin of error– useful for emphasis
• Bespoke modelling of potential policy impact– shows scale and sensitivity to base assumptions– timely and transparent
• Mathematical modelling– can we improve the mathematical fit and quantify
the underlying uncertainty?
Short term monthly projections
5,000
5,500
6,000
6,500
7,000
7,500
8,000
8,500
9,000
9,500
Apr 07 Jul 07 Oct 07 Jan 08 Apr 08 Jul 08 Oct 08 Jan 09 Apr 09 Jul 09 Oct 09 Jan 10 Apr 10 Jul 10 Oct 10 Jan 11 Apr 11
Historical data
Upper limit (95% CI)
Lower limit (95% CI)
Forecast
Scenario modelling
Impact of reducing the number of short sentences on prison places: 2010-11 data Reduction of 6 months or less 3 months or less 10% 50 10 20% 90 20 50% 240 50 Custodial disposal equivalent for one prison place 15 30
Scary mathematical model
0
r
0
s ),( (t)N , (t)N
0 ,
0 ,
0 ,0)(),(
dxxtn(t,x)n(t,x)dxn
(x)n,x)(n(t,x)ρx
n
t
n
(x)n,x)(n(t,x)ρx
n
t
n
(x) n,x)(n)(t,nxfxtρx
n
t
n
irs
rorrrr
ioiiii
sosisss
NB. mean & variance satisfy the same equations
Mathematical model - forecast
Jan95 Jan00 Jan05 Jan10 Jan15 Jan20 Jan255000
5500
6000
6500
7000
7500
8000
8500
9000
9500
10000
date
po
pu
lati
on
Total population projection vs time
Context is important - short sentences
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
1989-90 1992-93 1995-96 1998-99 2001-02 2004-05 2007-08 2010-11
Nu
mb
er
0
10
20
30
40
50
60
70
%
Proportion of very short sentences
Number of cases
Policy does not occur in a vacuum
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
1991 1993 1995 1997 1999 2001-02 2003-04 2005-06 2007-08 2009-10
Ave
rag
e d
aily
po
pu
lati
on
Total
Sentenced
Remand
Prisoners and Criminal Proceedings (Scotland) Act 1993: automatic release at halfway point of sentence (2/3 point for long-term prisoners)
Home detention curfew
Presumption against very short sentences
Introduction of supervised attendance orders
More stringent conditions for granting bail at Crown and court level (June 2006, December 2007 and June 2011)
Extension of 110-day rule for remand in high court
Increase in maximumsentence for sheriff solemn
Crown policy on knife crimesummary justice reform
Criminal Procedure (Scotland) Act 1995: increased penalties for offending while on bail
Are prison populations appropriate phenomena for forecasting?
Projected and actual population England & Wales 2001
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
1993 1994 1995 1996 1997 1998 1999 2000-01
2001 actual
Projected population for 2001
• Are drivers of prison growth like hurricanes or health care?
• What effects do projections have?
• What other options are there?
Three questions
• Defined drivers are unpredictable and unconnected to demographic change
• Other possible drivers excluded: prisons and projections
Like hurricanes or health care?
What effects do projections have?
• Are there any costs of getting it wrong?
• Power to make a future while estimating futures
• Quantification of fear?
Other options?
• Within statistics, ‘What If’ planning models
• Outwith statistics, ‘That’s What’ planning models
Scenario A = Scottish Prisons Commission target (91)
Scenario B = Norway becomes penal model for Scotland (78)
Scenario C = USA becomes penal model for Scotland (200)
-
2,000
4,000
6,000
8,000
10,000
12,000
2011-12 2012-13 2013-14 2014-15 2015-16 2016-17 2017-18 2018-19 2019-20
Current projections
Wha’s like us?
“In our grammar we have the future tense, which enables us to imagine and visualize a state of affairs different from the presently existing – a ‘matter’ with quite different ‘facts’… the only way of ‘predicting’ the future [is] to join forces and pool our efforts to cause future events to conform to what we desire.” (Zygmunt Bauman)
S Armstrong (2012) ‘The Quantification of Fear through Prison Population Projections’ available at: www.sccjr.ac.uk
