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From |
Joshua Mitts <joshua.mitts@yale.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Regression discontinuity with interrupted time series |

Date |
Wed, 6 Mar 2013 18:19:35 -0500 |

Hi Austin, Thank you for taking the time to reply in such depth. Let me try to clarify--I don't think I explained very clearly. I'm using a fuzzy RD design with a numeric cutoff that determines eligibility for the program. Treatment is taken by compliers at time t. I measure subjects at repeated intervals prior to and following treatment. The assumptions of non-manipulability of assignment variable, monotonicity, and exclusion are valid at time t. I could stay in the world of traditional RD and observe differences at t+5 minus t-5. But that seems unduly restrictive. If I assume a linear trend and could somehow control for autocorrelation, the additional outcomes at t+1, t+2, etc. would seem to provide useful data. These are, after all, affected by the treatment at time t too. ITS says I can compare trends pre- and post-treatment (with control group providing counterfactual over time), and RD gives local randomization with a non-manipulable arbitrary cutoff. It seems there has to be a way to combine these, e.g., regress change in pre- to post- trend on treatment dummy (w/eligibility instrument) weighted by proximity to numeric cutoff at time t. Thanks again, Josh On Wed, Mar 6, 2013 at 4:51 PM, Austin Nichols <austinnichols@gmail.com> wrote: > > Joshua Mitts <joshua.mitts@yale.edu>: > You need to be a lot more clear about your scientific model of the > data generating process. I have not read the cited paper, but I am > doubtful about the marriage of RD and ITS. The point of RD is that > outcomes of observations on either side of the cutoff are identical on > average except for treatment status so the jump in outcomes at the > cutoff is the effect of treatment; that is not true if you think > treatment has some dynamic impacts, or in other words the effect of > treatment increases (or decreases) in the assigment variable, so that > you do not want the instantaneous impact of treatment at the cutoff, > but some effect away from the cutoff. Imagine it this way: you have > an announcement event that affects stock prices at noon but you do not > want to compare stock prices at one minute after noon to noon because > you think the event actually changes the time path of investment and > you want changes in market valuation over some period until the > announced policy change takes place. This is no longer a good > situation for RD if you are thinking about comparing across time. You > can still use the dummy for above the cutoff at time t as a dummy for > treatment in periods after t, but the comparison will not have the > clean RD interpretation (where the counterfactual is essentially > observed if the data is dense around the cutoff) if you are using time > as an assignment variable. Can you assume linear trends before and > after time t? You can define time as time minus t so that the constant > is the jump in mean outcomes at t, and the dummy for above the cutoff > is the instrument for treatment; if they are perfectly collinear you > have a "sharp" design but you may want to also estimate a change in > trend after t for the treatment group, for which you may need an > additional instrument--the key here is how the cutoff is defined. Is > the variable that is compared to the cutoff subject to manipulation? > Changing over time? Only examined at time t? If you have an assigment > variable that is not time, you are back in the world of RD, and you > may be better off with a long difference in outcomes (reducing > problems due to measurement error in fixed effect models), e.g. y at > t+5 minus y at t-5, regressed on treatment in the usual RD manner. > > On Wed, Mar 6, 2013 at 11:00 AM, Joshua Mitts <joshua.mitts@yale.edu> wrote: > > Hi, > > > > How can I combine regression discontinuity with interrupted time > > series analysis in Stata? I have repeated observations of an outcome > > variable for ~180 units over time, an intervention at time t at a > > cutoff value, and more repeated observations post-intervention. With > > ordinary RD, I can only measure the outcome individually at t+1, t+2, > > etc. It seems this is an active area of research[1], but I'm not sure > > how to implement it in Stata. Any suggestions would be greatly > > appreciated. > > > > Thank you, > > Josh > > > > -- > > Joshua Mitts > > Yale Law School '13 > > joshua.mitts@yale.edu > > > > [1] Somers, Maree-Andre, Pei Zhu, Robin Jacob, and Howard Bloom. 2009. > > Combining Regression Discontinuity Analysis and Interrupted > > Time-Series Analysis. Grant #R305D090009. Washington, DC: Institute of > > Education Sciences, U. S. Department of Education. > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Regression discontinuity with interrupted time series***From:*Austin Nichols <austinnichols@gmail.com>

**References**:**st: Regression discontinuity with interrupted time series***From:*Joshua Mitts <joshua.mitts@yale.edu>

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