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I don't know if this is a problem. But wanted to make sure my model is free of "confounding"

I am doing a thesis on IPO underpricing, where I am using multiple regression.

The problem is from my regression (1) without dummy variables to regression(2) where I included some dummy variables, one of the independent variables became significant, which I am not sure of is a good thing.

In my regression (2) I include stock exchange dummy variables. I have 3 stock exchanges where I include 2 of them in my multiple regression while the last one is the reference point. Here one of my independent variables becomes significant.

Am I wondering if am doing something wrong or if this is ok?

I can post some data or the output if that helps.

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  • $\begingroup$ If this ever makes it out as an academic paper, please post it here. I would be interested. $\endgroup$ – Dave Harris Dec 17 '17 at 2:35
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It is important to remember that statistics is a branch of rhetoric and not a branch of math. When you are performing a regression analysis you are engaging in argument. It follows that the regression should follow from your argument and does not stand alone as an independent concept.

It is also important to remember that a p-value does not tell you if anything is true or that your model makes sense. A low p-value just tells you that you should be investigating the phenomenon.

Let us assume, for a moment, that you are suffering neither from a false positive or a false negative in your significance tests.

Without dummy variables, there is no underpricing. This is a finding. It is, in fact, a very important finding. With a dummy variable, it is significant. This implies that at least one, but not all of the exchanges have assets coming into them that are mispriced. If all had been mispriced, then the regression slope would have been significant, but the dummies would not have been.

This is also a finding.

There is a problem with your methodology, however. With Frequentist methods, you are assuming that your model is the true model in nature. You have two models. Both cannot be true. One is, or the other is. If the first model is true, then the exchanges do not matter. If the second is true, then the exchanges drive everything. There are specific differences in how the exchanges are structured so that those differences are facilitating mispricing.

You should perform either an AIC or BIC on your model, only do one. Choose it based on its properties and not by convenience. If the xIC chooses the model without the exchanges this would imply that while the exchanges were significant, they are a poor fit to the data generating function in nature. This would likely indicate that an outlier or set of outliers are driving the statistical significance. They are probably very large outliers. On the other hand, if the xIC chooses the later model, it would imply that the market microstructure is causing the mispricing. Please do note, this mispricing may not be real.

An implication that the market microstructure is causing a mispricing may imply that your understanding of what it means to be mispriced is incorrect. It may be that there exist market specific risks, probably through liquidity and price formation, that are present and that your thesis is incorrect. Instead, it would imply you would need to perform a far deeper investigation.

If that was the case, I would recommend reading:

Measures of Discount for Lack of Marketability and Liquidity, pp.474-507. The Valuation Handbook; Wiley Finance, John Wiley & Sons. 2010. Authors: Ashok Abbott

I would also look at the work out there on market making and price formation.

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  • $\begingroup$ "It is also important to remember that a p-value does not tell you if anything is true or that your model makes sense. A low p-value just tells you that you should be investigating the phenomenon.": I'd comment this depends on the purpose of testing. $p$-values make for bad exploratory analysis. Selection of confounder variables for adjustment should be based on apriori knowledge of the scientific question. $\endgroup$ – AdamO Dec 19 '17 at 23:00
  • $\begingroup$ @AdamO yes, I would agree with you on p-values being bad for exploratory work, but this does not appear to be exploratory. Also, using exchanges as controls makes scientific sense here even though the language in the question doesn't say that. Nonetheless, do you have a suggested edit for the sentence? $\endgroup$ – Dave Harris Dec 20 '17 at 1:25

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