Example: What is the background to the gender earnings gap

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Introduction

• Example What is the background to the gender
  earnings gap?
• Theoretical model or background
• The human capital theory. Observable differences
  such as educational investments or on-the-job
  training may be different (Becker, 1967).
• Theories of discrimination.
• Statistical discrimination. Discrimination in
  wage offers towards the group mean productivity.
• Preferential discrimination. Employers may have
  preferences for giving a lower wage to women,
  even if it is inefficient to do so.

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Empirical strategy

• Regression model
• - dependent variable.
• - independent variable.
• - random disturbance (measures all variables
  omitted in the regression model, all
  measurement errors, all functional form
  errors).
• - parameters to be estimated in the model.

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Example with Background to the Gender Gap in Wages

• lnW log of hourly wage rate.
• FEMALE binary (0, 1) indicator for being
  female.
• EDUC number of years of schooling.
• EXP number of years of work experience.

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Estimation strategy

• First step estimate the unconditional gender gap
  by only including the dummy variable for FEMALE
  in the equation.
• Second step include the EDUC variable.
• Third step include also the EXP variables.
• There are, in addition, lots of other potential
  variables that can be included.

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Presentation of data

• Data should be presented so that the study can be
  replicated by other researchers in the future.
• Data source. Such as LNU 1991.
• Population. What population do you make inference
  to?
• Sample size.
• How many observations were deleted and why?
• Table that defines the variables may be useful.
• Table containing descriptive statistics mean,
  standard deviation, max/min.

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Variable Description
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Descriptive Statistics
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Results

• Estimation results.
• Start with the most simple model in most cases
  the bivariate regression.
• Present then the alternative models.
• All results should be included in the same model.
• Discuss economic and statistical significance.
• Expected sign?
• Are the estimates statistically significant?
• What about the magnitude of the results? Economic
  significance.
• Joint significance tests? F-tests.
• Possible problems and caveats with the analysis?

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Table. Estimation results from earnings equation.
Dependent variable hourly wage rate. Number of
observations 2,249.
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Dummy variables

• The definition of a binary, or dummy, variable is
  that it is 1 if the individual has a particular
  property and 0 otherwise.
• The interpretation of the coefficient estimate
  for the dummy variable is the average difference
  controlling for the effect of the other
  variables.
• The interpretation of the coefficients of the
  other variables in the model is the average
  effect within the two groups defined by the dummy
  variable. Also possible to add more dummy
  variables to allow for more than two groups.

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Categorical dummy variables

• Example Levels of education instead of number of
  years of education.
• Level 1 Basic compulsory.
• Level 2 Vocational schooling.
• Level 3 Secondary education.
• Level 4 University.
• Make dummy variable for each education level such
  that
• Lev1 1 if Level 1 and otherwise 0 Lev2 1
  if Level2 and 0 otherwise ..
• We end up with four dummy variables for each
  level of education.

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Interactions

• An interaction variable is the product between
  two separately measured variables. Could be two
  binary variables, one binary and one continuous
  or two continuous.
• Relaxes the assumption of equal effects within
  groups.

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Example Differential returns to education for
males and females

• Add interaction between dummy variable for female
  and the years of schooling variable.

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Table. Estimation results from earnings equation.
Dependent variable hourly wage rate. Number of
observations 2,249.
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The Impact of Legalized Abortion on Crime

• John Donohue and Steven Levitt, Quarterly Journal
  of Economics, 2001.
• Steven Levitt and Stephen Dubner Freakonomics,
  2006, (available in both Swedish and English).

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Interactions between dummy variables

• Example Marriage premium

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There was a marked trend towards decreased crime
rate in the US during the 1990s. Why?

• Violent crimes increased by 80 percent in the
  period 1975-1990. Peaked in 1990.
• Rapid decrease in the crime rate in the early
  1990s.

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Candidates for explaining the big decrease
proposed in the public debate

• Increased number of police.
• Innovative police strategies.
• Increased reliance on prisons.
• Changes in crack and other drug markets.
• Aging of the population.
• Tougher gun control laws.
• Strong economy.
• All other explanations (increased use of capital
  punishment, concealed-weapons laws, gun buybacks,
  and others).

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Increased number of police

• Number of police officers increased by 14 percent
  in the US during the 1990s. Could that explain
  the drop in the crime rate?
• We use cross-section data and estimate the
  relation

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• When the crime rate increases, there is a demand
  for more police officers. Also, areas with a high
  crime rate tend to have more police officers.
  Leads to a positive correlation between number of
  police officers and the crime rate, i.e. ?gt0.
• Does this mean that more police officers leads to
  more crime?

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• Reversed causality
• Can the estimates be used for policy analysis?

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• One strategy is to add confounders to the
  model, here e.g. the unemployment rate.

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• To show causality, we need a scenario in which
  more police are hired for reasons completely
  unrelated to rising crime. If for instance police
  were randomly sprinkled in some cities and not in
  others, we could look to see whether crime
  declines in the cities where the police happen to
  land
• Freakonomics, page 126.

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• Famous study by Levitt Using Electoral Cycles
  in Police Hiring to Estimate the Effect of Police
  on Crime American Economic Review, 1997, page
  270-290.
• Uses the fact that a popular election strategy
  for the sitting mayor in US elections is to hire
  more police officers just before the elections to
  get the law-and-order votes.
• He compares the crime rate in cities just having
  elections with cities that did not have
  elections.

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• Elections unrelated to the underlying criminality
  (or the unemployment rate). Isolates the effect
  of extra police officers.
• Results there is an effect of the number of
  police men on the criminality rate, but it could
  only explain a tiny part of the over all decline
  in criminality during the 1990s.

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Increased use of capital punishment

• Some claim that the increased use of capital
  punishment deterred from committing crimes.
• Great methodological problems in estimating the
  effect of capital punishment similar to that of
  the effect of number of police officers.
• Upper bound estimate by Isaac Ehrlich who
  estimated that every execution deters 7 murders
  per year.
• 1991 14 executions and in 2001 66. The 52
  additional executions would have led to 364 fewer
  homicides. Less than 4 percent of the actual
  decrease in homicide rates.
• In addition, very few of those on death row
  actually get executed. Less than 2 percent
  execution rate per year. Not a very common cause
  of death for a US gangster!

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Legalization of Abortion

• Abortion was legalized in 5 US states in 1970
  (New York, California, Washington, Alaska,
  Hawaii).
• Roe vs. Wade
• Norma McCorvey (real name Jane Roe) living in
  Texas appeal the state law denying her the right
  to abortion to the Supreme court. The Supreme
  court decided the state law denying the right to
  abortion as unconstitutional. Lead to that
  abortion was legalized in the entire US in 1973.

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• Abortions increased enormously after Roe v. Wade.
  750.000 abortions in the first year after the
  verdict. In 1980 1.6 million abortions (1 on
  every 2.25 live births).
• Dramatic change in the composition of the
  population. The unborn children expected to be
  very different from the born. Observable factors
  like class, parental education, socio-economic
  status. Unobservable factors like being denied.

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• 1991 First cohort of children born after Roe v.
  Wade aged 17 (criminality most common in the
  age-group 17-24). Crime rates starts to decrease.
• 1992 The 17 year olds from 1991 are now 18 and a
  new cohort from the post Roe v. Wade era becomes
  17. Crime rate decreases even more.
• Donue and Levitt also compares the decrease in
  the crime rates in the states that legalized
  abortion already in 1970 with those that did so
  after Roe v. Wade.
• Legalization of abortion led to fewer unexpected
  children.
• Being unexpected increases the probability to
  commit crimes.
• Thus, legalization of abortion led to fewer
  crimes.

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Conclusions

• There are lots of examples of correlations that
  are interpreted as causal relations.
• Be critical and question the plausibility of the
  estimated effects.
• Look for alternative explanations and see to what
  extent each of them can contribute.