Regression kink design

3 key takeaways:

• A regression kink design identifies causal effects by exploiting changes in the slope of a policy or treatment rule rather than changes in the level.
• It is used when a policy or rule has a specific kink or threshold, creating a natural experiment for causal inference.
• RKD provides a robust method for causal analysis, especially in settings where traditional regression discontinuity designs are not applicable.

What is regression kink design?

Regression kink design is an empirical strategy used to estimate causal effects by focusing on changes in the slope of a regression function at a known point of kink in the policy or treatment rule. Unlike regression discontinuity design (RDD), which relies on abrupt changes in the level of the treatment variable at a cutoff, RKD relies on changes in the slope or gradient of the assignment rule.

For example, consider a tax policy where the marginal tax rate changes at a specific income threshold. The change in the tax rate creates a kink in the relationship between income and tax liability. By analyzing the change in behavior around this kink, researchers can infer the causal effect of the tax policy on labor supply or other economic outcomes.

Key components of regression kink design

Several key components define the regression kink design:

• Kink Point: The specific point at which the slope of the assignment rule changes. This point is critical for identifying the causal effect.
• Treatment Variable: The variable of interest affected by the policy or rule change. The treatment variable’s slope changes at the kink point.
• Outcome Variable: The dependent variable that the researcher is interested in studying to understand the causal impact of the treatment variable.

By focusing on the change in the slope at the kink point, RKD isolates the local causal effect of the policy or treatment.

Applications of regression kink design

Regression kink design can be applied in various fields to study causal relationships:

• Public Economics: Analyzing the impact of tax policies, welfare programs, or subsidies by examining changes in behavior at the points where the policy parameters change.
• Labor Economics: Studying the effects of minimum wage laws, unemployment benefits, or pension plans by exploiting kinks in the eligibility or benefit rules.
• Health Economics: Investigating the impact of health insurance policies or drug pricing regulations where changes in policy parameters create kinks in the treatment assignment.

These applications demonstrate the versatility of RKD in identifying causal effects across different policy contexts.

Advantages of regression kink design

Regression kink design offers several advantages:

• Causal Inference: RKD provides a robust method for identifying causal effects, especially in settings where other quasi-experimental designs are not feasible.
• Policy Relevance: By focusing on specific policy-induced changes, RKD directly addresses the causal impact of real-world policy interventions.
• Local Identification: RKD identifies local treatment effects around the kink point, providing precise estimates of the causal impact in the relevant range.

These advantages make RKD a powerful tool for empirical research and policy evaluation.

Challenges of regression kink design

Despite its strengths, regression kink design also faces several challenges:

• Data Requirements: RKD requires detailed data around the kink point to accurately estimate the slope changes and causal effects.
• Specification Sensitivity: The results of RKD can be sensitive to the choice of bandwidth and functional form, requiring careful robustness checks.
• Assumptions: RKD relies on assumptions such as the continuity of the potential outcomes and the absence of manipulation around the kink point. Violations of these assumptions can bias the estimates.

Addressing these challenges is essential for the valid application of RKD in empirical research.

Examples of regression kink design in action

Here are some examples illustrating the use of regression kink design:

• Tax Policy: Analyzing how changes in marginal tax rates at specific income thresholds affect labor supply decisions by workers.
• Welfare Programs: Investigating the impact of changes in benefit levels at certain income cutoffs on household spending and saving behaviors.
• Education Funding: Studying the effects of funding formulas that change at specific enrollment numbers on school performance and student outcomes.

These examples highlight how RKD can be applied to derive causal inferences from policy-induced changes in various fields.

Exploring related concepts such as regression discontinuity design, instrumental variables, causal inference, and quasi-experimental methods can provide further insights into the principles and applications of regression kink design in empirical research.