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I am quite new at (quasi) natural experiment analysis, so please bear with me, and got some questions.

In my research, I am planning to use one policy change which happened 2002 and treated firms are asset size with and over € 2 million and control group includes firms with assets less than € 2 million.

Policy change date is 2002.

Threshold: € 2 million.

I was wondering that according to this policy change, how can I decide to use Difference in Differences, Regression Discontinuity or both together? Is it appropriate to use just Difference in Differences or Regression Discontinuity?

Any help would be greatly appreciated.

Best regards,

Caroline

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  • $\begingroup$ Welcome to CV! I have some follow-up questions. First, have you investigated the trends in your outcome variable across time between the two groups? Do you observe firms across many time periods pre- and post-policy? Also, did you acquire data on a lot of firms at this financial cusp? $\endgroup$ – Thomas Bilach Jun 10 at 18:21
  • $\begingroup$ Thank you for your message. I will try to answer your questions to the best of my knowledge. I have not started my analysis exactly. Actually, before your question I was wondering whether if investigating the trends (empirically) a key part of the difference in differences or regression discontinuity analysis. Do I need to identify parallel paths between the control and treatment group before applying any model and how can I do it (on Stata)? $\endgroup$ – Caroline Fressard Jun 10 at 21:41
  • $\begingroup$ For detecting, control and treatment groups I just created a dummy variable. I have treated and control firms (created dummy variables) in many time periods. In addition, I collected many firm level (control) variables. $\endgroup$ – Caroline Fressard Jun 10 at 21:44
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You'd probably want to use a regression discontinuity (RD) design over a diifference in difference (DiD) design, though you may certainly want to include some year fixed effects or otherwise control for the time-component of your data.

To explain a bit about the intuition, DiD typically involves studying two groups over time, and one group gets treatment and the other control group doesn't. The key assumption is that had the group that received treatment not received it, it would have had the exact same effect as the control group. As such, in your case, it's not enough to compare firms with assets over 2 mil to those under, because larger asset firms presumably have a different trajectory compared to firms with assets under 2 mil.

Instead, your RD design focuses on your true source of 'quasi' randomness: assuming that firms did not know about this cutoff, they did not make any effort to be above or below the 2 mil threshold, in which case you can compare firms just above 2 mil to those just under. An RD design provides the framework to implement this. Intuitively, you could do a DiD comparing those just above to those just below the cutoff, but if the RD design holds, their pre-trends should be exactly the same (because we assume that firms around the cutoff are the same!), and so all you need to do is look at their future outcomes and don't care about their pre outcomes, but now you're just back in the RD framework, except that the RD framework focuses more on not just using the data at the cutoff, but your whole dataset.

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  • $\begingroup$ Thank you for the detailed answer. Actually, the papers which I replicate does not mention about regression discontinuity clearly but they classify firms as a treated (such as €2mil-€5mil), indirectly treated (assets €1mil-€2mil) and untreated (assets €500thousand - €1mil) according to the size of their assets and use DiD method. But It looks a bit Regression Discontinuity design so I am bit confused between the two methods. I did my analysis just according to shock date and threshold (tretated=>€2mil) by employing DiD. $\endgroup$ – Caroline Fressard Jul 6 at 18:40

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