# Thread: CARs from small sample(26): Which Regression is the best to perform?

1. ## CARs from small sample(26): Which Regression is the best to perform?

Dear All,

I am new to this forum, but I am trying to become more and more specified in statistics for my Master Thesis (Erasmus University Rotterdam, Netherlands)

Enough intro, my problem is the regression of my sample. I calculated Cumulative Abnormal Returns for 5 event windows, and I want to use SPSS to find if some variables (8 in total) influence the CARs.

I tried a normal linear regression, but also a Stepwise regression. The problem is that my significance values are way to low for this. After the performance of a stepwise regression, zero or maybe one variable stays in the results.

With this little information, does anyone of you guys have any tips or diretions to look into?

If additional data is needen, please ask me!

Thanks in advance!

2. ## Re: CARs from small sample(26): Which Regression is the best to perform?

Look at

Rit = a + b * Rmt + d*D + error

Then use d in a second stage with explanatory variables (firm characteristics; governance variables, sector dummies, whatever).

Look at Chandra and Balachandran (1992) for Portfolio WLS
Sefcik and Thompson (1986) for time series Portoflio GLS and Portfolio OLS

I recommend using (1) OLS with White robust errors (2) Portfolio WLS, as was applied in the recent Journal Finance paper on Investment Banking something-or-other that used Portfolio WLS from Chandra and Balachandran (1992).

For an application of Sefcik and Thompson look at Kristin Forbes 2004 paper, but this is for longer event windows oinly.

3. ## Re: CARs from small sample(26): Which Regression is the best to perform?

Also what's "small sample" - the number of firms or the time periods? This will guide model selection. (u can't use portfolio GLS with N > T )

Another thing to choose is what base regression you're to work with.,. Market model? Fama-French 3 factor model? 4 factor model? (i.e. famma-french + momentum)? Some other mdoel? of course market model abnormal returns is standard but fama-french sees some usage. If you're doing an "excess co-movement" type study (e.g. contagion), consider Ri = a + b Rm + c Rc + c D Rc + error, where Rc is the index returns that you're testing for excess comovement.

4. ## Re: CARs from small sample(26): Which Regression is the best to perform?

Dear derksheng,

First of all: Many thanks for the answers.

Second, I performed an event study by the hand of Seiler (2004):

Seiler, M. (2004). Performing Financial Studies: A Methodological Cookbook.
New Jersey: Prentice Hall.

My small sample consists out of 26 firms, with an event window of -15 to 15 where 0 is the announcement day for an acquisition.

Though I am not an expert on analysis, I performed the following regression where I use different event windows to find leakage/drift before and after the announcement. For the windows the regression looks like this:

Window -15 to -6 = a + Betavar1 * Var1 + ... + BetaVar7 * Var7 + Error

The main questions are: Is this correct or just stupid?

Second question: I was not expecting striking results (due to the 26 sample size) but for a particular variable I got: Coefficient: -5,24 with a T-stat of: -1,892* which is significant on the 10% level, so I got little significance performing the regression this way! But I was wondering if this is the correct way to do it

What do you think of it?

Many thanks in advance!

5. ## Re: CARs from small sample(26): Which Regression is the best to perform?

The methodologies I recommended in my post don't involve regressing the CAR in a cross-sectional regression.

They involve regressing the estimated coefficients of the breakpoint Dummies.

6. ## Re: CARs from small sample(26): Which Regression is the best to perform?

BUt if you want to use the CAR, look at Karafiath (1994), and look at a 2012 paper in the Journal of Finance that uses Portfolio WLS (from Chandra and Balachandran 1992) using CARs as the dependent varibale. It's called "investment banking relationships ..." something somethign.

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