Required assumptions Regression discontinuity design

1 required assumptions

1.1 testing validity of assumptions

1.1.1 density test
1.1.2 continuity of observable variables
1.1.3 falsification tests

1.1.3.1 predetermined variables
1.1.3.2 other discontinuities


1.1.4 inclusion , exclusion of covariates

required assumptions

regression discontinuity design requires treatment assignment random @ threshold treatment. if holds, guarantees barely received treatment comparable barely did not receive treatment, treatment status random.

treatment assignment @ threshold can random if there randomness in assignment variable , agents considered (individuals, firms, etc.) cannot manipulate treatment status. example, if treatment passing exam, grade of 50% required, example valid regression discontinuity design long grades random, due either randomness of grading or randomness of student performance.

students must not able manipulate grade determine treatment status. 2 examples include students being able convince teachers mercy pass them, or students being allowed re-take exam until pass. in former case, students barely fail able secure mercy pass may differ barely fail cannot secure mercy pass . leads selection bias, treatment , control groups differ. in latter case, students may decide retake exam, stopping once pass. leads selection bias since students decide retake exam.

testing validity of assumptions

it impossible definitively test validity if agents able determine treatment status. however, there tests can provide evidence either supports or discounts validity of regression discontinuity design.

density test

mccrary (2008) density test on data lee, moretti, , butler (2004).

mccrary (2008) suggested examining density of observations of assignment variable. if there discontinuity in density of assignment variable @ threshold treatment, may suggest agents able manipulate treatment status.

for example, if several students able mercy pass , there more students barely passed exam barely failed. similarly, if students allowed retake exam until pass, there similar result. in both cases, show when density of exam grades examined. gaming system in manner bias treatment effect estimate.

continuity of observable variables

since validity of regression discontinuity design relies on barely treated being same barely not treated, makes sense examine if these groups similar based on observable variables. earlier example, 1 test if barely passed have different characteristics (demographics, family income, etc.) barely failed. although variables may differ 2 groups based on random chance, of these variables should same.

falsification tests
predetermined variables

similar continuity of observable variables, 1 expect there continuity in predetermined variables @ treatment cut-off. since these variables determined before treatment decision, treatment status should have no effect on them. consider earlier merit-based scholarship example. if outcome of interest future grades, not expect scholarship affect earlier grades. if discontinuity in predetermined variables present @ treatment cut-off, puts validity of regression discontinuity design question.

other discontinuities

if discontinuities present @ other points of assignment variable, these not expected, may make regression discontinuity design suspect. consider example of carpenter , dobkin (2011) studied effect of legal access alcohol in united states. access alcohol increases @ age 21, leads changes in various outcomes, such mortality rates , morbidity rates. if mortality , morbidity rates increase discontinuously @ other ages, throws interpretation of discontinuity @ age 21 question.

inclusion , exclusion of covariates

if parameter estimates sensitive removing or adding covariates model, may cast doubt on validity of regression discontinuity design. significant change may suggest barely got treatment differ in these covariates barely did not treatment. including covariates remove of bias. if large amount of bias present, , covariates explain significant amount of this, inclusion or exclusion change parameter estimate.

recent work has shown how add covariates, under conditions doing valid, , potential increased precision.