The impact of prison on crime

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The impact of prison on crime
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The incapacitation effect of prison depends on

• the rate at which offenders commit crime when
  free
• the likelihood of an offender being caught and
  convicted
• the likelihood, if convicted, that an offender
  will receive a prison sentence
• the average time spent in prison and
• the likelihood of an offender resuming his or her
  involvement in crime once he or she is released
  from prison

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The level of incapacitation (I) is given by

• I ?qJS Tr/(Tr S)
• 1 ?qJS Tr/(Tr S)
•  where
•  I the fraction of crimes avoided as a result
  of incapacitation
• ? the rate at which offenders commit crimes
• q the probability of being apprehended and
  convicted for a crime
• J the probability of being sentenced to prison
  if convicted
• S the average time spent in custody
• Tr the average time offenders will remain
  involved in crime

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The change in prison numbers required to produce
a one per cent fall in crime (E) is given by

• E 1 ?qJS2TR/(TR S)2
• - ?qJSTR2/(TR S)2

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Key assumptions.

• Accurate estimates of the model have been
  obtained.
• All offenders run the risk of being arrested and
  incarcerated.
• The more offenders we imprison, the fewer there
  are in the general population
• The experience of imprisonment does not change
  the expected length of a criminal career (Tr) or
  the rate at which individuals offend (?)

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The assumed parameter values are

• ? (the average number of burglaries per annum)
  38.1
• q (the annual risk of a burglar being apprehended
  and convicted) .045
• J (the probability of a convicted burglar
  receiving a prison sentence) .44
• S (the average period spent in custody by
  imprisoned burglars) 1.02
• TR (average residual criminal career length)
  4.1 years

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The change in prison numbers required to produce
a one per cent fall in crime (E) is given by

• E 1 ?qJS2TR/(TR S)2
• - ?qJSTR2/(TR S)2

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Summary of findings

• Prison does prevent a lot of burglary
• The prison population would have to be increased
  by more than 34 to reduce the number of
  burglaries by another 10 per cent
• This would cost at least 26 million per annum
• There may be more cost-effective ways of getting
  the burglary rate down but we do not know because
  the cost-effectiveness of most law and order
  policies is unknown.