Quantitative Methods

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• Quantitative Methods Week 4
• Application
• Stephen Levitts Where Have
• All the Criminals Gone?

Roman Studer Nuffield College roman.studer_at_nuffiel
d.ox.ac.uk
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Where Have All the Criminals Gone?

• List all the variables that Lewitt looks at in
  the course of the chapter

• unemployment rate.
• number of criminals sent to prison.
• length of prison sentences.
• number of executions.
• number of police officers.
• number of guns.
• price of cocaine.
• innovation in police techniques (dummy variable).
• number of conceptions.
• number of births.
• number of abortions.
• number of children living in poverty.
• number of single parents.
• average age of total population

• number of crimes.
• state.
• year.
• number of violent crimes.
• number of financially motivated crimes.
• number of homicides.
• number of homicides involving a gun.
• number of drug related homicides.
• economic growth.
• gender of criminals
• ethnicity of criminals.
• age of criminals.

? What are the level of measurements, what are
the basic units of observations (cases)? Are all
ratio measurements?
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Where Have All the Criminals Gone?

• Many factors (variables) are potentially
  associated with the drop in crime rates in the
  US. Where does he find correlations between a
  variable and the falling crime rate? Which
  variables are positively, which ones negatively
  correlated with the crime rate variable? Where
  does he find no correlation?

Concept/Variable
Measured Variable
Correlation
No correlation
Strong economy
Unemployment rate, growth rate
Negative 33
Reliance on prisons
Number of prisoners
Capital punishment
Number of executions
No correlation
Negative (but) 10
Number of police
Number of policemen
No correlation
Innovative policing strategies
..
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Where Have All the Criminals Gone?
Concept/Variable
Measured Variable
Correlation
Tougher gun laws
Brady act,
No correlation (in the present context)
Negative 15
Changes in crack market
Price of crack
Aging of population
??
No correlation
Legalizing abortion
Number of abortions
Negative The rest? About 50
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Where Have All the Criminals Gone?

• In which cases does Lewitt move from correlation
  to causation? How does he justify this change in
  language? Is it convincing?
• Does this chapter potentially suffer from a
  omitted variable problem? Of what other factors
  can you think for explaining the fall in crime
  rates?
• For each potential factor, he provides both the
  relevant data and some common sense explanation.
  What do you believe more the data or the
  explanations? Why does he need the explanations
  at all?
• Are you convinced by Lewitts overall argument?
  Has the fall in crime rate in the US herewith
  been explained once and for all?

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Where Have All the Criminals Gone?
Source Bureau of Justice Statistics,
http//www.ojp.usdoj.gov/bjs/glance.htmCrime
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Again Caution when Interpreting Correlation
Results!!

• Correlation is NOT causation!!
• Causation is very hard to ascertain in social
  sciences
• Beware of spurious or nonsense correlation!
• Examples
• Simultaneous decline of birth rates and of the
  number of storks in Sweden
• Positive correlation between shoe size and income
  level
• Omitted variables are one of the big problems in
  econometrics

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Caution when Interpreting Correlation Results (II)

• Watch out for the influence of outliers on the
  correlation results!!
• Example GDP per person and purchasing power
  around the world, 2007

• Very strong association
• Positive correlation
• r 0.95

• Just 2 outliers
• Weak association suggested
• r 0.34

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Computer Class

• Replicating Levitts Results with US
  Macroeconomic Data

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US Macro Dataset

• We will no try to replicate some of Levitts
  results using national statistics from the US
• Sources U.S. Department of Justice, Bureau of
  Justice Statistics US Census Bureau
• Variables Crime (total and rates), number of
  prisoners, abortion rate, education,
  unemployment, poverty
• Get dataset at http//www.nuff.ox.ac.uk/users/stud
  er/teaching.htm

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Exercises

• Data set and descriptive statistics
• Open dataset and convert the Excel dataset into a
  Stata dataset
• Look at each of the variables in turn
• Produce appropriate graphs Get a first
  visualisation of the data does it look normally
  distributed?
• Produce nice graphs including titles, etc.
• Compute the mean, median, standard deviation,
  coefficient of variation, kurtosis and skewness
  for every variable
• How do the different crime variables compare?
  Which one do you take for the correlation
  analysis?
• Correlation analysis
• Look at the association between crime and the
  other variables
• Make a scatter plot to get a first impression of
  their association Do you think these variables
  are connected? Positively/negatively?
• Calculate the correlation coefficient how would
  you explain the result?
• If you look at the scatter plot, are there any
  outliers?

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Exercises (II)

• Save your data set and your results on the O
  drive
• Save your new data set as a Stata file (.dta)
• Export and save your data set as an Excel file
  (.xls)
• Copy your results and save them in a word file
  (.doc)

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Appendix STATA Commands

• correlate varlist Displays all the pairwise
  Pearson correlation
• coefficients between the variables listed
  after
• correlate
• pwcorr varlist Like correlate, but has some
  additional options like calculating the
  significance level
• spearman varlist Displays Spearman's rank
  correlation coefficients for all pairs of
  variables
• scatter varname1 varname2 Produces a scatter
  plot with variable 1 on the x-axis and variable
  2 on the y-axis

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Homework

• Readings
• Feinstein Thomas, Ch. 4
• Problem Set 3
• Finish the exercises from todays computer class
  if you havent done so already. Include all the
  results and answers in the file you send me
• Do exercise 3 from Feinstein Thomas, p. 91
  (using Relief dataset)