Great! Identifying the assignment variable with a clear cutoff is the absolute cornerstone of a successful Regression Discontinuity (RD) study.

What is an Assignment Variable in RD?

The assignment variable (also known as the "running variable," "forcing variable," or "score") is a continuous variable that determines who receives the "treatment" (the intervention, policy, or program of interest) and who does not.

The clear cutoff is a specific point on this continuous variable. Individuals who fall on one side of this cutoff receive the treatment, while those on the other side do not. The crucial insight of RD is that individuals just above and just below the cutoff are very similar in all unobserved characteristics, making the "treatment" status effectively random at that point.

Examples of Assignment Variables with Clear Cutoffs:

Here are common categories and specific examples to get your ideas flowing. Think about the variable, the cutoff, and the resulting treatment:

1. Education & Academic Performance:

• Assignment Variable: Standardized test score (e.g., state achievement test, college entrance exam, end-of-course grade).


• Cutoff: A specific score needed to pass, qualify for an advanced program, receive a scholarship, or avoid remedial classes.


• Treatment: Enrollment in an advanced math class, receipt of a merit scholarship, placement in a remedial reading program, promotion to the next grade.


• Outcome: Future academic performance, college enrollment, earnings.


• Assignment Variable: GPA or course average.


• Cutoff: A specific GPA threshold for academic probation, dean's list, or eligibility for certain extracurriculars.


• Treatment: Being placed on academic probation, receiving special counseling, being eligible for a sports team.


• Outcome: Future GPA, graduation rates, disciplinary actions.


• Assignment Variable: Student attendance rate.


• Cutoff: A percentage (e.g., 90%) below which interventions are triggered.


• Treatment: Mandatory parent-teacher conferences, truancy officer visits, eligibility for school events.


• Outcome: Improved attendance, academic performance.

• Assignment Variable: Income level (e.g., household income, individual earnings).


• Cutoff: The official poverty line, a specific income threshold for eligibility for social welfare programs, housing subsidies, or food stamps.


• Treatment: Receipt of food stamps, eligibility for Medicaid, access to public housing, tax credits.


• Outcome: Health outcomes, consumption patterns, employment.


• Assignment Variable: Age (e.g., years, months).


• Cutoff: Legal drinking age, voting age, minimum age for specific social security benefits, age for school entry.


• Treatment: Legally allowed to drink alcohol, vote, receive retirement benefits, start kindergarten.


• Outcome: Alcohol-related accidents, voter turnout, health spending, educational attainment.


• Assignment Variable: Disability score / Severity index.


• Cutoff: A score determining eligibility for disability benefits or specific support services.


• Treatment: Receiving disability payments, access to specific medical equipment or therapy.


• Outcome: Employment, health status, quality of life.

• Assignment Variable: Medical test score or biomarker (e.g., blood pressure reading, cholesterol level, BMI, A1C score for diabetes).


• Cutoff: A specific level that triggers a diagnosis or treatment protocol (e.g., hypertension diagnosis, pre-diabetes, obesity).


• Treatment: Prescription of medication (e.g., statins, blood pressure medication), referral to a specialist, enrollment in a weight management program.


• Outcome: Future health outcomes (heart attack, stroke, weight loss), healthcare costs.


• Assignment Variable: Disease severity score (e.g., a mental health assessment score, cancer staging score).


• Cutoff: A score dictating eligibility for a specific type of therapy, surgery, or palliative care.


• Treatment: Receiving a particular surgical procedure, intensive psychotherapy, hospice care.


• Outcome: Mortality, quality of life, recurrence rates.

• Assignment Variable: Credit score.


• Cutoff: A score determining eligibility for a loan, a specific interest rate, or a particular credit card product.


• Treatment: Receiving a loan, getting a lower interest rate, qualifying for a premium credit card.


• Outcome: Debt levels, bankruptcies, spending patterns.


• Assignment Variable: Company revenue/profit.


• Cutoff: A threshold determining eligibility for small business subsidies, specific tax breaks, or increased regulatory scrutiny.


• Treatment: Receiving a government subsidy, lower tax burden, undergoing a more rigorous audit.


• Outcome: Business growth, employment, investment.

• Assignment Variable: Judge's "leniency score" or a criminal risk assessment score.


• Cutoff: A score that dictates sentencing guidelines or parole eligibility.


• Treatment: Longer vs. shorter prison sentence, being granted parole.


• Outcome: Recidivism rates, future employment.


• Assignment Variable: Election vote share (e.g., incumbent's vote share).


• Cutoff: 50% (winning vs. losing).


• Treatment: Winning the election (being in office).


• Outcome: Future policy decisions, economic growth, re-election chances. (Note: this is sometimes considered a "fuzzy" RD if the actual assignment isn't perfectly deterministic at 50% due to recounts, ties, etc., but often treated as sharp).

Key Characteristics of a Good Assignment Variable for RD:

As you consider your options, keep these in mind:

• Truly Continuous or Quasi-Continuous: It needs to be a variable where people can fall just above or just below the cutoff. Discrete variables with few values don't work well.


• Clear, Unambiguous Cutoff: There must be a definite, known point where treatment status changes. No fuzzy lines or subjective interpretations.


• Deterministic Assignment (for Sharp RD): Crossing the cutoff must perfectly determine treatment status. If treatment is only more likely after crossing the cutoff, that's a "Fuzzy RD" design, which is more complex but also valid.


• No Manipulation Around the Cutoff: Individuals (or those who assign treatment) should not be able to precisely manipulate their score to fall on one side of the cutoff versus the other just barely. For example, if students know a specific score gets them into an honors class, they might try harder to achieve exactly that score, or teachers might inflate grades for students just below. This introduces selection bias.


• Relevance of the Cutoff ONLY for Treatment: The cutoff itself should not directly affect the outcome except through its impact on treatment status. For example, if turning 18 makes you eligible to vote and receive a specific government grant unrelated to voting, that's problematic.

To help you further, tell me:

• What general domain or area are you interested in studying? (e.g., education, health, public policy, economics, criminal justice, etc.)


• What kind of "treatment" or intervention are you thinking about? (e.g., a specific program, a policy change, a medical procedure).