Question

3 Application questions. 40 points conditions to be able to use the regression 1. Explain in detail the necessary obtain causal results
Econometrics please answer

Answer 1

Regression discontinuity design requires that treatment assignment is "as good as random" at the threshold for treatment. If this holds, then it guarantees that those who just barely received treatment are comparable to those who just barely did not receive treatment, as treatment status is effectively random.

Treatment assignment at the threshold can be "as good as random" if there is randomness in the assignment variable and the agents considered (individuals, firms, etc.) cannot perfectly manipulate their treatment status.

Students must not also be able to perfectly manipulate their grade so as to perfectly determine their treatment status. Two examples include students being able to convince teachers to "mercy pass" them, or students being allowed to re-take the exam until they pass. In the former case, those students who barely fail but are able to secure a "mercy pass" may differ from those who just barely fail but cannot secure a "mercy pass". This leads to selection bias, as the treatment and control groups now differ. In the latter case, some students may decide to retake the exam, stopping once they pass. This also leads to selection bias since only some students will decide to retake the exam.

It is impossible to definitively test for validity if agents are able to perfectly determine their treatment status. However, there are some tests or conditions that can provide evidence that either supports or discounts the validity of the regression discontinuity design.

Density test

McCrary (2008) suggested examining the density of observations of the assignment variable. If there is a discontinuity in the density of the assignment variable at the threshold for treatment, then this may suggest that some agents were able to perfectly manipulate their treatment status.

Continuity of observable variables

Since the validity of the regression discontinuity design relies on those who were just barely treated being the same as those who were just barely not treated, it makes sense to examine if these groups are similarly based on observable variables. For the earlier example, one could test if those who just barely passed have different characteristics (demographics, family income, etc.) than those who just barely failed. Although some variables may differ for the two groups based on random chance, most of these variables should be the same.

Predetermined variables

Similar to the continuity of observable variables, one would expect there to be continuity in predetermined variables at the treatment cut-off. Since these variables were determined before the treatment decision, treatment status should have no effect on them. Consider the earlier merit-based scholarship example. If the outcome of interest is future grades, then we would not expect the scholarship to affect earlier grades. If a discontinuity in predetermined variables is present at the treatment cut-off, then this puts the validity of the regression discontinuity design into question.

Other discontinuities

If discontinuities are present at other points of the assignment variable, where these are not expected, then this may make the regression discontinuity design suspect. Consider the example of Carpenter and Dobkin (2011) who studied the effect of legal access to alcohol in the United States. As the access to alcohol increases at age 21, this leads to changes in various outcomes, such as mortality rates and morbidity rates. If mortality and morbidity rates also increase discontinuously at other ages, then it throws the interpretation of the discontinuity at age 21 into question.