Event Study Regression - "omitted because of collinearity"

[Arthur Jones]

Hi
Im running a regression for a event study.
My data essentially consists of daily returns for one currency, and daily returns for a currency index for 21 days - 10 days before and 10 days after the event.

(the currency is turkish lira per usd, and the currency index is simply the average of 7 major currencies against the dollar)

i then generated 21 dummy variables, one for each day, and its 1 for that observation, and 0 otherwise.

essentially, im regressing the currency returns upon the index returns and all the dummy variables. the coefficient of each dummy variable gives me the abnormal return for that day.

However, when i run the regression, stata drops the index returns and the 21st dummy variable. Even if i shorten the event window i get the same response.

Any ideas whats going wrong here??

[Arthur Jones]

should i run a newey west regression??

[Clyde Schechter]

Back to basics. When you have a discrete variable with n levels, to use it in a regression, you must use n-1 indicator ("dummy") variables to represent it. That's because if you use all n indicators, they will always add up to 1, because in any observation exactly one of them is one and the rest are zero. So if you use all n indicators, they are colinear among themselves. That makes the regression model unidentified. Stata (and most other statistical packages) handle this situation by simply dropping one of the indicators and informing you that it has done so.

Then there is the problem of your index being dropped. The problem here is that the index values are in 1-1 correspondence with the days in your data set. So if you know the day, the index value is automatically determined--and this too is colinearity. If your day indicators are named d1, d2, through d21, then the following linear equation holds:

index on day i = value of index on day i * di (because di = 1 on that day)

which in turn = sum j = 1 to 21 (value of index on day j * dj), because dj = 0 if j != i.

Even after dropping one of the day indicators, you still get colinearity, because if you drop indicator dk, the constant term of the regression then fills the role of dk in that equation.

So you have several colinear relationships among the predictor variables in your model and there is no choice but to resolve them by dropping things.

All of that said, I think you are approaching this incorrectly anyway. I do not work in finance, and I'm not sure I really understand the concept of abnormal returns, but from what I've seen here on the Forum, my understanding is that you get abnormal returns just by regressing the currency on the index and then calculating the residual. You do not use time indicators when doing that. So it's just:

regress turkish_lira currency_index
predict abnormal_return, resid

[Arthur Jones]

Thank you for your reply!

Your first point is definitely valid - i believe its called the dummy variable trap.
However, regarding the methodology - of course i am a newbie so could be wrong. But i am following the following methodology outlined by equation 1 in the following paper:
"using dummy variables in the event methodology, Imre Karafiath 1988"

i believe i have followed the steps outlined in the papers methodology.


However, i will do some more research and will get back to you on my progress.

in the meantime, if anyone else with basic knowledge w.r.t event studies notices any glaring errors, do comment!

[Clyde Schechter]

using dummy variables in the event methodology, Imre Karafiath 1988"

This is an international and multidisciplinary forum. This article may well be folklore in your circle, but to many of us, including me, it is a mystery. When providing references here it is best to provide complete citations that anybody can look up.

[Arthur Jones]

n.b. copying/pasting the name onto google will give you the article, or this link will:
https://doi.org/10.1111/j.1540-6288.1988.tb01273.x

[Clyde Schechter]

Thanks for the link. Unfortunately, only the abstract is available directly there; the article itself is behind a paywall. The journal is not one that my institution's library provides access to, so I'm afraid I can't say more.

Nevertheless, I am 100% confident that the index variable is being dropped for the reason I gave in #3 and that it is not possible to simultaneously include the index and the time indicator variables in a model. Perhaps the article mentions this problem and advises some way of handling it. But I guarantee you that the solution necessarily involves omitting something or imposing some identifying constraint on the relationships among the coefficients. You can't defeat linear algebra.

My suggestion on how to calculate abnormal returns was, as I indicated, based only on what I have seen done here on the Forum and I don't have any confidence that it is correct--only that I have seen others use it here.

[Arthur Jones]

its available here also- https://www.researchgate.net/publica...nt_Methodology (no paywall)

I think you're correct. The problem lies in my methodology. I dropped observations in the estimation window (which are observations before the event window), and so havent calculated market returns in the estimation window?

Do you think this may be the source of my issue? I believe this is where i have deviated from the methodology listed in the paper above.

n.b. only need to read page 2, and 1st two paragraphs of page 3

[Arthur Jones]

Ok. Now i have no omissions.
I also calculated daily returns and daily market returns over 100 days starting before the event window, in addition to the same returns+market returns i initially had.

Now, running the regression of returns upon market returns and 21 dummy variables yields no omissions because of colloinearity.

i believe this issue may have been solved. thank you for all of your help clyde.