# Regression discontinuity design versus panel cointegration

I have a panel data (21 years) and I am trying to figure out whether I should use regression discontinuity design (RDD) or panel cointegration. I do have a randomness in the assignment variable and so I don't have any problem using the RDD; I can examine the causality (local average treatment effect). My questions are: first, why one should use RDD over the panel cointegration; second how can the causality from the RDD be linked with the Granger causality resulting from the panel cointegration (assuming that there is the cointegration and hence it is possible to estimate the vector error correction model). As far as I understand, when you have assignment variable and that variable is random, you always use RDD (although it is possible to use panel cointegration), but if you don't have an assignment variable and that variable is not random or if you don't have an assignment variable, then you proceed with the panel cointegration. I would really appreciate if you could let me know whether my understanding is correct. Please suggest the papers if possible. Note that my dependent variable is in growth form (e.g. growth of wealth)in RDD, but if I have to use panel cointegration, I will have dependent variable in level form for long run and in growth form for short run.

Example: Let's suppose, I have a binary variable (treat) and the dependent variable is y. There are two different approaches in RDD: non parametric and parametric approach. In parametric approach, we use all observations and then the coefficient on the treat is called as causal effect (we can also use other control variables) .

In cointegration approach, we use all observations and we can examine the long run relationship between treat and y (plus other variables). However, the concern here is that variable treat is binary while other variables (dependent and control variables) are continuous. I test all continuous variables and found to be integrated of order 1. But, I am not sure whether it is to test for the unit root of variable treat (binary variable). Does it make any sense?. This is important before we decide to use cointegration since it should all varaibles should be integrated of order 1. How do I incorporate the varaible treat in the cointegration? How can I then compare the results of cointegration and RDD?

• Some more details would be nice, e.g.: what question are you trying to answer? Broadly speaking, cointegration deals with long run relationships and, at least to my experience, RDD is used to estimate treatment effects, so without further information it's hard to answer your question.
– KOE
Feb 3, 2014 at 22:01

From your question it seems like you want to estimate the effect of a treatment variable on some outcome variable. If that is indeed the case, a cointegration analysis won't do you much good. Here's why: You say that your treatment variable is binary variable, so I take it it takes the value 1 if an individual was treated and 0 otherwise. You are correct in your hesitation regarding the unit root testing of that variable; it's not meaningful. Think especially in terms of cointegration and how it is defined.

We say that two processes, $X_t$ and $Y_t$, say, are cointegrated when both are integrated of some order larger than zero but there exist a linear combination of them that is integrated of a lower order. But if one of them is constant over time, cointegration not possible since a constant is trivially stationary. Each treatment dummy in your data (one for each cross-section dimension / observed individual) is indeed constant over time.

With that in mind, RDD seems like the better choice. However, RDD is not always implementable (you need some sort of discontinuity to exploit, for one) so in general you cannot have a rule saying "either I do cointegration testing or exploit an RDD design". It all depends on the data you have or can get hold of. This is also what I mean in my comment: if you want advice on which approach to use, you have to give some details about what data you have and which question are you trying to answer.

Edit:

In response to your comment: the party membership of the governor cannot be cointegrated with the level of environmental expenditure because it cannot be integrated of any order $p>0$. Even if the value changes over time AND between individuals, the variable only takes two values and, thus, cannot include a stochastic trend. In order to be cointegrated with the dependent variable, they must share the same stochastic trend, but they cannot possibly do that, then.

• Thank you Karl. I am trying to see whether I can apply cointegration in this context: sciencedirect.com/science/article/pii/S0095069611000325. I hope you will update the answer once you go through the paper. The dependent variable I want to use is in level form and not the growth form as in the paper. As you will see, my treatment variable varies across time and state. Feb 4, 2014 at 18:08
• I skimmed the paper but from what I can see the authors are using a standard RDD design. Without going into too much detail; which variable is it that you were hoping to be cointegrated with the dependent variable?
– KOE
Feb 4, 2014 at 19:36
• Thanks once again. The paper is using Growth rate of environmental expenditure per capita as the dependent variable. I guess they avoid using level of expenditure because that may be I(1). So, I am wondering if it is possible to examine the same objective, i.e., the effect of (Di) the party membership of the governor on the level of environmental expenditure per capita using cointegration. Feb 4, 2014 at 19:59