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What is: regression discontinuity design?. Mike Brewer University of Essex and Institute for Fiscal Studies Part of “Programme Evaluation for Policy Analysis” (PEPA), a Node of the NCRM. Regression discontinuity design: overview.
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What is: regression discontinuity design? Mike Brewer University of Essex and Institute for Fiscal Studies Part of “Programme Evaluation for Policy Analysis” (PEPA), a Node of the NCRM
Regression discontinuity design: overview • A regression discontinuity design is a way of undertaking causal inference, usually of some policy intervention • It can provide robust, convincing estimates of causal impacts under fairly weak conditions or minimal assumptions • It was invented by psychologists, but labour economists are now realising how applicable it is • The nature of the intervention will determine whether an RDD is appropriate. Even when it is, data demands are often great
What is regression discontinuity? • A regression discontinuity design is appropriate where • a treatment/intervention/policy is given to individuals for whom some measured characteristic lies on one side of a “cut-off” (sharp RD) • AND the characteristic cannot be perfectly manipulated by individuals
(Sharp) regression discontinuity design These people are above the cut-off and exposed to treatment. To estimate the impact of the treatment, we need a comparison group Treatment,Di 1 X (running variable) 0 An ideal comparison group would have the same values of X, but not be treated, But such people do not exist... These people are below the cut-off and not exposed to treatment. And some of them are very similar to some who are treated... c (cut-off)
RDD: the principle • Compare treated outcome for those just above cut-off with untreated outcome for those just below cut-off • This identifies the average treatment effect on subjects at the cutoff • Why does this work? • If the “running variable” cannot be perfectly manipulated, then individuals on either side of the cut-off should be very similar to each other in their observable and unobservable characteristics: it’s as if treatment were randomly assigned • Key assumption: nothing else jumps at cut-off
RDD: examples See much longer list in Lee and Lemieux, 2010
RDD: implementation • Graphical analysis • Outcome vs running variable either side of cut-off
Example: link between entitlement to UB and length of unemployment Source: Lalive, (2007)
RDD: implementation • Graphical analysis • Outcome vs running variable either side of cut-off • Formal estimate • Parametric = OLS. Easy! • Non-parametric means local linear regression
RDD: implementing in OLS Indicator for being right side of cut-off, so coefficient measures how outcome variable jumps at X=c Allows running variable, X, affects outcomes according to quadratic function whose slope changes at X=c If X discrete, then should allow for errors to be clustered at level of running variable (Card and Lee, 2008) Other covariates
RDD: implementation • Graphical analysis • Outcome vs running variable either side of cut-off • Formal estimate • Parametric = OLS. Easy! • Non-parametric means local linear regression • Sensitivities and robustness checks
RDD: checks • Something other than treatment might cause the jumps • Do pre-treatment variables or explanatory variables jump around cut-off? • Individuals might manipulate running variable • Is density of running variable smooth around cut-off? • Do pre-treatment variables or explanatory variables jump around cut-off? • Distinguish between discontinuity and non-linearity • Are results robust to inclusion of higher-order polynomials? • Are results robust to changing size of “window” around cut-off? • Are there jumps when none expected (“placebo RDDs”)?
A non-smooth density function From McCrary, 2008. Probability of vote just being lost is a lot lower than it just being won
RDD: checks • Something other than treatment might cause the jumps • Do pre-treatment variables or explanatory variables jump around cut-off? • Individuals might manipulate running variable • Is density of running variable smooth around cut-off? • Do pre-treatment variables or explanatory variables jump around cut-off? • Distinguish between discontinuity and non-linearity • Are results robust to inclusion of higher-order polynomials? • Are results robust to changing size of “window” around cut-off? • Are there jumps when none expected (“placebo RDDs”)?
Variant: Fuzzy RDD • Fuzzy RDD appropriate when the probability that someone is treated changes discontinuously when a characteristic crosses a “cut-off” • For those close to the cut-off, “being on the right side of the cut-off” is a valid instrument (predicts treatment well, no direct impact on outcome) • Can then estimate impact of treatment through 2SLS (change in outcome either side of cut-off divided by change in treatment either side of cut-off) • Technically, requires a monotonicity assumption and then identifies a LATE: the impact of the treatment on “compliers” at the cut-off
Fuzzy regression discontinuity design Treatment,Di Di 1 X 0 c (cutoff) Now treatment depends on whether X bigger than cut-off c, but this is not the only factor. There is a jump in the fraction who are treated as we cross the cut-off, c.
Variant: Fuzzy RDD • Fuzzy RDD appropriate when the probability that someone is treated changes discontinuously when a characteristic crosses a “cut-off” • For those close to the cut-off, “being on the right side of the cut-off” is a valid instrument (predicts treatment well, no direct impact on outcome) • Can then estimate impact of treatment through 2SLS (change in outcome either side of cut-off divided by change in treatment either side of cut-off) • Technically, requires a monotonicity assumption and then identifies a LATE: the impact of the treatment on “compliers” at the cut-off
RDD: assessment • RDDs can provide convincing causal estimates and can be easily implemented via OLS • But • not universally applicable: depends entirely on nature of intervention • focusing on small area around cut-off often requires large amounts of data
References and reading Where it all came from: Thistlethwaite & Campbell, 1960 "Regression-Discontinuity Analysis: An Alternative to the Ex Post Facto Experiment" Journal of Educational Psychology, 51(6): 309-17 To find out more: Angrist & Pischke, “Mostly Harmless Econometrics” Lee and Lemieux, 2010, "Regression Discontinuity Designs in Economics." Journal of Economic Literature, 48(2), 281–355 Journal of Econometrics, 2008, 142(2), esp. articles by Imbens & Lemieux, Lalive, Card & Lee, McCrary: http://www.sciencedirect.com/science/journal/03044076/142/2. For economics examples, see citations in Lee and Lemieux Some UK examples outside economics: Del Bono et al., “Health information and health outcomes: an application of the regression discontinuity design to the 1995 UK contraceptive pill scare case”, ISER WP 2011-16 Eggers and Hainmueller, “MPs for Sale? Returns to Office in Postwar British Politics”, American Political Science Review, 103, pp 513-533