Crime and Punishment in the American Dream

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Crime and Punishment in the American Dream

• Rafael Di Tella,
• HBS

• Juan Dubra,
• Universidad de Montevideo

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• A striking aspect of American social and economic
  organization is the harsh treatment of criminals.
• As Tonry (1998) describes them, "Contemporary
  policies concerning crime and punishment are the
  harshest in American history and of any western
  country
• Tonry (1998) opens the introductory chapter to
  The Handbook of Crime and Punishment with
  "American punitiveness is not the result of
  higher crime rates or of a steeper increase in
  crime in recent years. For most serious crimes,
  America's rates are not the highest among Western
  countries (Mayhew and van Dijk 1997), and other
  countries experienced equally sharp increases in
  crime rates during the 1970s 80s. The
  difference is attributable to crime and
  punishment entanglement in American politics."

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Punitiveness and IncomeGDP per Capita
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Punitiveness and InequalityGini Coefficient
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Punitiveness and Beliefs I Poor Can Escape
Poverty?
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Punitiveness and Beliefs IIPoor are Lazy?
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Punitiveness and Beliefs IIIGovernment doing too
little to help poor?
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Punitiveness and Beliefs IVGovernment or
Employees should manage Business?
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Crime Rates OECD
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A Model

• Three players
• Individuals (work or crime)
• Firms
• Government

• 1st Stage
• Workers choose effort
• Firms choose contracts
• 2nd Stage
• Workers stay honest or choose crime
• Government chooses punishment

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1st Stage
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Our Notion of Effort pays

• a) Effort pays because, if the firm chooses
  market technology, then effort (for the worker)
  pays. This belief is confirmed in equilibrium.
• b) The bigger is p, the more true this is.

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1st stage Two equilibria

• French (effort no pay)
• Firms offer flat contracts
• Workers exert no effort
• all receive uM

• American (effort pays)
• Firms offer risky contracts
• Workers exert effort
• p lucky (get uH )
• 1-p unlucky (get uL )

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2 Theories of Punishment

• Deterrence
• Punish to prevent/deter future mischief.
  Incapacitation is sometimes considered to be a
  subset of specific deterrence
• We think it is discredited (except
  incapacitation)
• Used in several economics papers

• Retribution
• punish to restore the social order by action
  against the criminal. Associated with the phrase
  an eye for an eye, a tooth for a tooth. Basis
  for Code of Hammurabi
• In modern times, California has been the most
  explicit in embracing the retributive justice
  model. In 1976, Governor Jerry Brown signed the
  Determinate Sentencing Law, which made
  retribution the sole objective of the state's
  sentencing system "The Legislature finds and
  declares that the purpose of imprisonment for
  crime is punishment."

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We model Punishment as

• Based on Retribution.
• This means that the government must set a
  punishment to match the meanness of the
  population of criminals. Hence, we need to know
• What are the posterior (conditional on the
  individual being a criminal) beliefs of the
  Government. This will be derived from the
  economic system and the prior distribution of
  tastes for crime in the population.
• What is the Governments utility function.

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Example 2nd stage Americap 1, r 0

• criminals
• uH - u

• Taste shock for worker µ
• Commit crime iff
• honest lt crime
• uH lt u µ
• u utility from probability of
• getting caught, bounty,
• Jail time if caught
• Signal lifetime prospects

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2nd stage France

• criminals
• uM - u

• Taste shock for worker µ
• Commit crime iff
• honest lt crime
• uM lt u µ

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France America

• uH - u
• Posterior of types given crime
• (shift up a lot)

Density f of µ uM
- u Posterior of types given crime (shift up a
little)
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Comparison of Posteriors

• America
• America has
• worse criminals
• France
• uM - u uH
  - u

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2nd stage America

• With probability p, lucky
• criminals
• uH - u
• With prob. 1-p, unlucky
• criminals
• uL - u

• Taste shock for worker µ
• Commit crime iff
• honest lt crime
• Lucky uH lt u µ
• Unlucky uL lt u µ
• u utility from probability of
• escaping, bounty minus jail time if caught
• Signal lifetime prospects

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2nd stage France

• criminals
• uM - u

• Taste shock for worker µ
• Commit crime iff
• honest lt crime
• uM lt u µ

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France America

• p. f
• p
• uH - u
• (1-p). f
• 1-p
• uh - u
• pf (1-p)f f
• (1-p). f

Density f of µ uM
- u Posterior of types given crime
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Comparison of Posteriors

• America
• France
• uL - u uM - u uH - u

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Intuition

• w angels
• x good
• y sinners
• z evil
• w

• France
• gF (evil criminal)
• America
• gA (evil criminal)
• x y z

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Recap, 2nd Stage Simultaneous Choice of
Strategies

• Individuals choose cutoffs (for their crime
  decisions). Call them c, and they do not depend
  on u in the sense that if u changes, the action
  space does not change.
• In America there are p lucky and 1 p unlucky.
  The lucky choose a cutoff cH and the unlucky cL
  In France there is only one cutoff cM
• Only the optimal cutoffs depend on u in the
  sense that uH - u and uL - u change with u
• Any cutoff c (cH, cL) results in a posterior
  gc.
• The optimal cutoffs will depend on the
  Governments choice of punishment, u .

• The Government chooses a punishment level t.
• The Governments expected utility depends on the
  distribution of types of criminals, which in turn
  depends on c (cH, cL), the cutoffs chosen by
  the workers.
• For each s there is an optimal t, t(c)

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2nd Stage Government Sets Punishment

• Retribution Choose t to Max
• gc is the governments posterior belief about the
  parameter µ (meanness) conditional on being a
  criminal, and a choice of cutoffs c.
• q(.) is an increasing function representing the
  disruption in the social order imposed by a
  criminal of type µ
• Solution is

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Main Result (calibration)

• For a reasonable set of parameters (e.g., uH
  1.5, uL0.5, uM1, p0.9, r0, and utilities and
  distribution for µ) we find that
• Punishment is more severe in America
• There is higher crime in France
• Of course, with differential discrimination,
  ghettos, guns, etc, you can increase both crime
  and punishment in America. Crime opportunities.

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3 extensions yield more crime in America

• p different from p(the truth). p sets punishment
  whilst the truth sets total crime
• Matching total crime opportunities may be fewer
  than total disposition for crime
• Crime rate in America is committed by both blacks
  and whites. Thus we are only about white crime
  and punishment.
• Levitt (2004) plus Table 1, suggests this is
  pointless

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Result 2 Comparative Statics

• When belief in the American dream intensifies
  Punishment becomes harsher
• When there is less poverty (uL increases) crime
  decreases and punishment increases

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Conclusions

• We document a correlation between beliefs in
  the American dream and punitiveness
• We model two identical countries choosing
  different economic systems (technologies/
  contracts, effort levels).
• In the American equilibrium the distribution of
  wealth is more unequal, so the resulting pool of
  criminals is more disperse, with more mean
  criminals that in France.
• It is then possible to obtain equilibria where
  there is more punitiveness in America.

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Notes on crime rates
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Punitiveness and BeliefsLeft wing
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How to model American dream

• Our choice
• A given level of effort results in a higher
  probability of high output, and hence a higher
  prob of high utility uH
• Our choice changes average income in the country
  (and the relative numbers of rich and poor).

• Other choice
• An upward movement of uH
• This would also increase the average income of
  the country (but keep the relative numbers of
  rich and poor constant).
• A bigger belief in the American dream would now
  have an ambiguous effect on desired punishment.
  BUT, result obtains either with convex q(.) or
  having only a few of the potential criminals
  actually taking on crime.