Regression Discontinuity

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Regression Discontinuity

• Course Applied Econometrics
• Lecturer Zhigang Li

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Impact of Air Pollution on Housing Values (Chay
and Greenstone, 2005)

• How much does air quality (pollution) affect the
  value of housing?
• Conventional Hedonic Approach
• PiaAirißQiui
• Q Other observed characteristics of housing,
  e.g. number of bedrooms, neighborhood public
  service (school quality), other local amenities
  (black-white ratio), etc.
• Problems
• Unobserved factors that are related to both air
  pollution and housing prices, e.g. urbanization,
  income, crime rates, population densities, etc.
• Reverse causality
• Heterogeneous consumers and self-selection
• Finding weak and variant effects (elasticity is
  about -.06)

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Impact of Test-based School Evaluation Systems
(Chay et al., 2005)

• A typical way to allocate resources to schools is
  to link them to school quality measured by mean
  test scores.
• In order to evaluate the outcome of the allocated
  resources, researchers often estimate the
  following model
• ?Yia?Fundiß?Xiei
• Problems
• Mean test scores are noisy measures of school
  quality
• The noises may be mean reverting

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Endogeneity due to Mean Reverting

• Suppose the extra funding has no effect on school
  performance (Y)
• Y1Yµ1
• Y0Yµ0
• ?YY1-Y0µ1-µ0
• ?Fundf(Y0)f(Yµ0)
• Cor(?Y,?Fund)gt0

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P-900

• P-900 is a program in Chile that provided extra
  fund during 1990-1992 to help low-performing
  schools.
• Building repairs
• Cheaper instructional materials
• Teacher training
• After-school tutoring
• Funding criteria
• Use average test scores in 1988 to measure school
  quality
• Only schools with quality lower than some cutoff
  lines were funded

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Solution Using Regression Discontinuity Design

• Observe that
• Cor(?Y,?Fund) is a smooth function of Y0.
• P-900 assignment is a discrete function of 1988
  average test scores.
• Implication 1 We may approximate the smooth
  function
• Implication 2 We may restrict our estimation
  sample within arbitrage narrow bands around the
  cutoff level.

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Alternative Augmented Models

• Model 1
• ?Yia?Fundiß?XiY0iei
• Model 2
• ?Yia?Fundiß?XiY0iY0i2Y0i3ei
• Model 3
• Use the eligibility for the funding program as
  the instrument for ?Fundi in the two models above.

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Further Issues

• Selection The government assign funding based on
  unobserved factors
• Solution Use eligibility by P900 criteria as IV.
• Sorting Families respond to P900 by moving their
  children from untreated to treated schools.
• Solution Control for school characteristics

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