Key Concepts of Regression Discontinuity Designs to Know for Causal Inference

Regression Discontinuity Design (RDD) is a powerful method in causal inference that estimates treatment effects by focusing on a specific cutoff in a continuous variable. It helps identify causal relationships when random assignment isn't possible, making it a valuable tool in research.

1. Definition and basic concept of Regression Discontinuity Design (RDD)

   • RDD is a quasi-experimental design used to estimate causal effects by exploiting a cutoff point in a continuous running variable.
   • Individuals just above and below the cutoff are assumed to be similar, allowing for causal inference about the treatment effect.
   • It is particularly useful when random assignment is not feasible, providing a way to approximate experimental conditions.

2. Sharp vs. Fuzzy RDD

   • Sharp RDD occurs when treatment assignment is strictly determined by whether the running variable crosses a threshold.
   • Fuzzy RDD allows for some individuals to receive treatment even if they do not meet the cutoff, leading to a probabilistic treatment assignment.
   • The distinction affects the estimation of treatment effects and the interpretation of results.

3. Assumptions and requirements for valid RDD

   • The running variable must be continuous and the assignment to treatment must be based solely on the cutoff.
   • There should be no other confounding factors that influence the outcome at the cutoff.
   • Individuals cannot be able to manipulate their position relative to the cutoff.

4. Bandwidth selection and local linear regression

   • Bandwidth refers to the range of data around the cutoff used for analysis; a smaller bandwidth can lead to more precise estimates but may reduce sample size.
   • Local linear regression is often employed to estimate treatment effects within the selected bandwidth, providing a flexible approach to modeling.
   • The choice of bandwidth can significantly impact the estimated treatment effect and should be chosen carefully.

5. Testing for manipulation of the running variable

   • It is crucial to test whether individuals can manipulate their running variable to gain access to treatment.
   • Common methods include examining the density of the running variable around the cutoff and conducting formal tests for manipulation.
   • Evidence of manipulation can invalidate the assumptions of RDD and compromise causal inference.

6. Graphical analysis and visualization in RDD

   • Graphical representations, such as scatter plots, can help visualize the relationship between the running variable and the outcome.
   • A clear discontinuity at the cutoff in the outcome variable indicates a potential treatment effect.
   • Visualizations can also aid in assessing the validity of assumptions and the robustness of results.

7. Sensitivity analysis and robustness checks

   • Sensitivity analysis involves testing how results change with different bandwidths, functional forms, or estimation methods.
   • Robustness checks help confirm that findings are not driven by specific assumptions or outliers.
   • These analyses enhance the credibility of the causal claims made through RDD.

8. Limitations and external validity of RDD

   • RDD is limited to local treatment effects around the cutoff and may not generalize to other contexts or populations.
   • The design relies heavily on the assumption that no other factors influence the outcome at the cutoff.
   • External validity concerns arise when considering the applicability of findings beyond the specific setting of the study.

9. Applications and examples of RDD in various fields

   • RDD has been applied in education (e.g., evaluating the impact of scholarship programs based on test scores).
   • It is used in public policy to assess the effects of eligibility criteria for social programs.
   • Health economics often employs RDD to study the effects of interventions based on age or income thresholds.

10. Comparison of RDD with other causal inference methods

    • Unlike randomized controlled trials (RCTs), RDD does not require random assignment but still aims to estimate causal effects.
    • RDD is often compared to propensity score matching, which attempts to create comparable groups but may not account for all confounding variables.
    • Instrumental variable (IV) methods can also be contrasted with RDD, as both aim to address endogeneity but do so through different mechanisms.