Natural Experiments

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Natural Experiments

• Course Applied Econometrics
• Lecturer Zhigang Li

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Natural Experiment

• Natural experiment is an application of the
  matching method with more strict condition
• NE required the control and treatment groups to
  be matched not only by observed factors, but also
  unobserved factors.
• Whether unobserved factors are matched is
  inferred from theory and other observed
  information.

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How much is the return to education?

• Return to education
• What is the value of Schooling?
• Do people really learn useful things in schools?
• Do people learn more in college than in high
  school?
• Should government spend more money on schools?
  What level of schools should get more funding?

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How hard is it to measure the return to
education?

• A naïve regression
• IncomeiaEducationiei
• Problems
• Measurement Errors (Income, Education)?
• Underspecification?
• Functional form misspecification?
• Endogeneity?

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Key Issue

• Endogeneity is the key issue
• Due to the correlation between education and
  omitted variables that affect income (talents,
  family environment, )
• Due to measurement errors in education
• The problem may not be solved by adding more
  control variables or using panel data.
• Can matching solve the endogeneity problem?

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Identical twins

• Arguments for using twins data
• Identical twins should be equally smart they
  should look similar and they should have the
  same family background.
• Therefore, if we could find twins with different
  education, we can compare their income. The
  difference should reflect only the effect of
  education but not of omitted variables.
• Strictly speaking, we assume there is no
  unobserved inter-twin difference that is
  correlated with education.
• Is this assumption valid?

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Solution with identical twins

• How about measurement error?
• A rule If one has two independent measures of a
  variable and both measures contain classical
  measurement errors, then she can use one measure
  as the instrumental variable of the other.
• Hence, one possible way to address the potential
  measurement errors in schooling is to ask the
  twins to report their co-twins education levels.

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An Empirical Study(Bonjour et al., 2003)

• Data 3,300 same-sex twins in 1999 in U.K.
• Detailed medical information
• Socioeconomic information
• Method
• ln(wif)ßSifaifeif
• ln(w1f)-ln(w2f)ßWTP(S1f-S2f)(a1f
  -a2f)(e1f-e2f)
• aif indicates ability
• A key question Why identical twins may have
  different years of schooling?

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What is the Effect of Minimum Wage Law? (Card and
Krueger, 1994)

• Do employers respond to an increase in the
  minimum wage?
• Design
• Event Minimum wage in New Jersey rose from 4.25
  to 5.05/hour on April 1, 1992.
• Design 1 The treatment group includes stores in
  NJ and the control group includes stores in PA,
  which was not (directly) affected by the wage
  rise.
• Design 2 Treatment includes stores paying high
  wage and control group includes stores paying low
  wage prior to the wage rise, all in NJ.

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Empirical Implementation

• Data Survey (employment, wage, prices) of 410
  (100) fast-food restaurants in NJ and eastern PA
  before and after the wage rise. Information on
  store closing also available.
• ?EiabXicGAPiei
• ?Ei Employment change at store i
• Xi Characteristics of store i
• GAP 0 for PA stores and high-wage NJ stores
  (5.05-W1i)/W1i for other NJ stores

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Issues

• Other things happening in NJ?
• Recession in NJ about the same time
• Other things happen in PA?
• Are NJ and PA comparable?
• Seasonal patterns and market structure similar
• Measurement
• Impact on store closing and opening.

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Findings

• No evidence that the rise in NJs minimum wage
  reduced employment
• In both design, increase in minimum wage increase
  employment.
• Prices of fast-food meals increased in NJ
  relative to PA. Within NJ, no evidence that
  prices increased more in stores most affected by
  the minimum-wage rise.

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Re-evaluating the Evidence by Card and Krueger
(Neumark and Wascher, 2005)

• Data
• Actual payroll (work hours) from 230 Burger King,
  KFC, Wendys, and Roy Rogers restaurants in NJ
  and PA.
• Data sample matched to the same zipcodes and
  restaurant chains of CKs study.

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Findings

• Standard deviation of employment change in CKs
  data is three times as large as the NW data,
  suggesting potential quality problem of the CK
  data.
• Estimates of the employment effect of the NJ wage
  rise lead to opposite conclusion from that of CK.
  Employment decrease in NJ after the wage rise.

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Do Better Schools Increase Housing Prices?
(Black, 1999)

• Compare prices of houses on opposite sides of
  attendance district boundaries
• Assumption the houses share similar neighborhood
  characteristics
• ln(price)aXßZd?teste
• Problem Not all relevant house or neighborhood
  characteristics can be observed (e.g. public
  goods, neighborhood characteristics)
• Solution Replace the district characteristics
  variable Z by a full set of boundary dummies
  indicating houses with common borders.

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Data

• Housing prices
• All purchases and sales from 1993 through 1995
  for three counties in suburbs of Boston,
  Massachusetts.
• Massachusetts is chosen because of its small
  school districts, reducing heterogeneity of
  population within districts.
• Focus on elementary schools because only this
  level allows for enough within-district
  variation.
• Neighborhood characteristics
• School district characteristics
• School Quality is measured by the fourth grade
  Educational Assessment Program.

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Sensitivity Tests

• Concern Districts on opposite sides of the
  boundaries are very different.
• Exclude boundaries that were railroad tracks,
  highways, major streets.
• An artificial natural experiment to account for
  progressions in neighborhoods towards good
  schools.
• Compare the effects of including more
  neighborhood controls on estimates.
• Compare housing characteristics across borders.
• Compare the effect of larger and smaller houses.

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