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Quantitative Methods – Week 4:
Application:
Stephen Levitt’s “Where Have
All the Criminals Gone?”
Roman Studer
Nuffield College
[email protected]
“Where Have All the Criminals Gone?”
• List all the variables that Lewitt looks at in the course of the chapter
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.
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
 What are the level of measurements, what are the basic units of observations
(cases)? Are all ratio measurements?
“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
Strong economy
Unemployment rate, growth rate
No correlation
Reliance on prisons
Number of prisoners
Negative [33%]
Capital punishment
Number of executions
No correlation
Number of police
Number of policemen
Negative (but…)
[10%]
Innovative policing
strategies
……..
No correlation
“Where Have All the Criminals Gone?”
Concept/Variable
Measured Variable
Correlation
Tougher gun laws
Brady act, …
No correlation
(in the present
context)
Changes in crack market
Price of crack
Negative [15%]
Aging of population
Legalizing abortion
??
Number of abortions
No correlation
Negative
[The rest? About 50%]
“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 Lewitt’s overall argument? Has the fall in
crime rate in the US herewith been explained once and for all?
“Where Have All the Criminals Gone?”
Source: Bureau of Justice Statistics, http://www.ojp.usdoj.gov/bjs/glance.htm#Crime
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
Caution when Interpreting Correlation Results (II)
• Watch out for the influence of outliers on the correlation results!!
150
100
50
0
0
50
100
Purchasing Power Parity
150
200
200
Example: GDP per person and purchasing power around the world, 2007
0
20000
40000
GDPperhead
60000
Very strong association
Positive correlation
r = 0.95
80000
0
20000
40000
GDP per head
60000
Just 2 outliers
Weak association suggested
r = 0.34
80000
Computer Class:
•
Replicating Levitt’s Results with
US Macroeconomic Data
US Macro Dataset
• We will no try to replicate some of Levitt’s 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/studer/teaching.htm
Exercises
A.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?
B. 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?
Exercises (II)
C. 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)
Appendix: STATA Commands
•
correlate varlist
•
pwcorr varlist
•
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
Displays all the pairwise Pearson correlation
coefficients between the variables listed after
correlate
Like correlate, but has some additional options
like calculating the significance level
Homework
Readings:
• Feinstein & Thomas, Ch. 4
Problem Set 3:
Finish the exercises from today’s computer class if you
haven’t 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)