Predicting Takeover Targets: Matching Samples

[Wesley Mokkink]

Dear all,

Currently I am conducting research on predicting takeover targets for US Public firms. I am planning to generate a model that estimates the probability whether a company is a target or not. To do so, I am considering to conduct a binomial (conditional?) logistic regression with the following outcomes: 0: Non-target; 1: Target. The independent variables that will be incorporated in the model, are listed in the attachment.

To eventually come up with an in-sample probability, I need to combine the target company data with the non-target company data. Since the difference between the number of companies in the target and non-target companies is quite extreme (11,628 vs. 2,078), it might be better to match these companies somehow. The way I think is appropriate to match the target observations with the non-target observations, is by year, SIC (Standard Industrial Code), and size (as proxied by total assets).

I hope someone can help me to find an appropriate way to match the targets with non-targets and hence estimate the chance of a company being a target (takeover probability).

Thanks in advance for your time/help!

Yours faithfully,

Wesley

[Mike Lacy]

I have a couple of questions:
1) I have a guess, perhaps incorrect, that you intend to sample the non-targets as opposed to using all of them. If so, I'd recommend against it and see this previous thread:
http://www.statalist.org/forums/foru...-help-required

2) Regardless of 1): What do you think that matching will do for you that using the same variables as ordinary control variables without the conditional model will do? I mention this because using conditional logit on a matched sample will make predicting probabilities, as opposed to relative odds, more difficult.

Regards, Mike

[Wesley Mokkink]

Mike Lacy Thank you for your fast reply! I appreciate your link to bankruptcy prediction literature, these two fields are indeed very similar methodology-wise. I based my methodology on the key paper in the field of takeover prediction, namely that of Palepu (1986). Like most other papers, he makes use of a state-based sample to enhance the predictive ability of the model.

There is valid econometric justification for preferring a state-based sample over a random sample in the estimation of an acquisition model because the number of targets is very small compared to the number of non-targets in the population. If a random sample were to be drawn from such a population, the sample would be likely to consist of an overwhelming majority of non-targets and very few targets. The 'information content' of such a sample for model estimation is quite small, leading to relatively imprecise parameter estimates. The sample can be enriched informationally by making the sample proportions of targets and non-targets more evenly balanced. A state-based sample accomplishes just this (Palepu, 1986, p.6)

He also mentions in the paper, that a state-based sample is a close-to-optimal design. However, I do not know how to create such a state-based sample in Stata.

Regards,

Wesley

References:
Palepu, K. (1986). Predicting Takeover Targets: A Methodological and Empirical Analysis. Journal of Accounting and Economics, 8, 3-35.

[Mike Lacy]

What you have quoted from this article sounds incorrect, at least as judged out of context. The reason to sample the non-targets is if obtaining information from them is prohibitively expensive. If you already have data on them, the cost of using them is 0. It is true that there are diminishing returns to precision in having more non-targets in the sample, but when you already have the data in hand, that's not relevant. Or, if it was prior to data collection, and you only had a fixed amount of money/time to spend on data acquisition, yes, the outcome-selective approach is desirable, presuming you can handle the difficulties of getting predicted probabilities out of such a sample. Again, I'd refer you to the previous StataList discussion, and to the vast literature on "case-control" studies in epidemiology, and possibly to my own (dated) article:

Lacy, M. G. 1997 "Efficiently Studying Rare Events: Case-Control Methods for Sociologists." Sociological Perspectives 40, 1: 129-154

(I cite some of the econometric literature there. I don't treat the work for social scientists written by Gary King, which postdated mine.)

[Wesley Mokkink]

Mike Lacy Thanks again! I read some excerpts from your paper and I saw that you cited some papers that Palepu (1986) also used (e.g., Manski & McFadden (1981)). Moreover, I like the intuitive way of explaining things in your paper.
Please correct me if I'm wrong, but how I understand it, is that I should not bother matching the non-targets with targets, but rather run an ordinary logistic regression on the entire sample.

[Mike Lacy]

Wow, you're a quick study! My best guess would be not to match: Using your control variables as covariates in an ordinary logistic regression should control them almost as effectively as would matching, and be simpler. Any matching would reduce the sample size, and thus reduce precision. Now, I suppose it's possible that matching might do a somewhat better job of controlling for those covariates, but I think the loss of precision would outweigh that advantage. This question, though, is better answered by other people on StataList who are more expert on this this topic than I am. You might want to post this as a different question on the list, something like "Choosing matching vs. conventional statistical control variables in logistic regression," and explain again the context of your question while referring to this discussion thread. I'd be interested to hear what people here say.