Slide 17 最近の更新履歴 Keisuke Kawata's HP

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Econometrics

Regression discontinuity design: Example

Keisuke Kawata

IDEC

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Question

True of false: you should suppose pure-random sampling data.

1. To obtain unbiased estimator by using RDD, discontinuous jump of treatment is needed.

2. To obtain unbiased estimator by using RDD, discontinuous jump of outcomes is needed.

3. To obtain unbiased estimator by using RDD, the running variable must not have direct impacts on outcome.

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Graphical image of IV

Explained variable Explanation

variables

Error term Instrumental

variables

Instrument relevance

Instrument exogeneity

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Graphical image of RD

Explained variable Explanation

variables

Error term Running

variables

“ all ha ge of ru i g aria le must have no effects.

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1

^st

example: Angrist and Lavy ( 99 QJE )

Purpose: Effect of class size on education achievement

Data: Survey for students (4^th and 5^th graders) in Israeli elementary schools. Outcomes: Test score of mathematics and reading.

Treatments: Class size. Empirical strategy:

Source of bias: Endogenous class asignment

⇒ The allocation of students for class are determined by teachers. lo a hie e e t stude ts ay e allo ated to s all size lass.

Fuzzy RD

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I stru e tal aria le: predi ted lass size

• The maximum class size is 40 (Maimonides rule).

⇒ Predi ted u er of lass are

⇒ predi ted lass size= ^�

� �

Total number of student in a school Predicted number of class

1^～40 1

41^～80 2

81^～121 3

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Graphically check of relevance: 4

^th

grade

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Graphically check of relevance: 5

^th

grade

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Estimation model

• 2SLS estimation. 1^st stage:

�� _� � � �� _�, �_�

= + ∗ � �� + ∗ �

2^nd stage:

� _� �� _�, �_� = + ∗ �� + ∗ �

Standard IV approach: using whole sample

RDD approach: Using samples with +5/-5 enrollments at discontinuous jump.

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OLS results

Thumb rule for significance: If the (absolute) value of estimated coefficient is more than twice for estimated standard deviation, this estimator is significant with 5%.

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IV and RDD results

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IV and RDD results

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2

^nd

example: Political resource curse?

Resource : Foreign aid, budget transfer, and revenue from natural resource.

→may bring good impacts. ^⇔ may also have bad impacts. e.g.,) Resource cause: Dutch disease hypothesis

Resource

Currency exchange rate _↑ Exporting industry _↓ Economy

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2

^nd

example: Political resource curse?

Political resource curse: Distri utio of resour e ay ause politi al i sta ility and corruption.

Resource

Bad political outcome: instability, corruption

Economy

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Crost et al (14 AER)

Purpose: Effect of development program on civil conflict. Data: Municipality level data in Philippines.

Outcomes: The number of casualties by civil conflict. Treatments: Eligibility of a development program.

Empirical strategy: RDD(running variable: Relative Poverty rank)

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KALAHI-CIDSS program

Community-driven development program: to enhance local infrastructure, governance, participation, and social cohesion.

Target: poor u i ipalities. Process:

Check eligibility Social preparation phase

To participate the program, set up the required institutional infrastructure (e.g., village meetings)

Program phase

Receiving large grand (6000$ per village) to construct local public goods.

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Targeting area

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Empirical strategy

•Eligibility is determined by the poverty level of municipalities.

•Authors estimate the relative poverty level; if the level is less than zero, the municipal can participate the program.

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Relationship between poverty level and program

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Check the assumption

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Empirical strategy: outcome

• Outcome is the number of casualties.

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Empirical strategy

• Parametric model

� ⁼ ⁺ � � ⁺ � ⁺ � ⁺ � � ⁺ � � ^{+ + +} �

where _� is outcome in municipality i in province p in phase t, _� is poverty level, and _� is dummy: =1 if _� ≤ 0 and dummy: =0 if _� > 0

• Nonparametric approach is also used.

Note: Even if a municipality has eligibility, they may not join program.

⇒If interest is the effect of program, _� should be used as IV.

Ho e er, authors’ i terest is the i pa ts of eligi ility , there y esti ati g i pa ts of eligibility.

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Check the assumption

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Main results

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Main results

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Final examination

• Date: July 30, 14:35^～ (1 hour), Place: 206

• After reading assignment paper, summarizing paper.

• No book and course material examination ^⇒ You can bring just writing implement (and your brain).

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Homework

Make a summary of following paper;

Alesina, A., Giuliano, P., & Nunn, N. (2011). Fertility and the Plough. American Economic Review, 101(3), 499-503.

⇒I will collect summary seat in 28, July.

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Reference

Angrist, J. D., & Lavy, V. (1999). Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement. The Quarterly Journal of Economics, 114(2), 533-575.

Crost, B., Felter, J., & Johnston, P. (2014). Aid under fire: Development projects and civil conflict. The American Economic Review, 104(6), 1833-1856.