Good evening,
I am currently working on my master thesis document and I do have a potentially basic question.
I try to understand the impact of having female in the acquirer's board of directors on the premium paid during an acquisition (percentage of price paid above or under the real value of the target).
To do so, I tried to perform an OLS on 800 observations (R Studio) but I kept finding heteroskedasticity in my model (even by transforming the data).
I tried to perform a plm regression but I keep having heteroskedasticity according to either the residual vs. fitted plot or the bptest. Additionnaly, the variable I try to analyse does have a p-value of 0.8 rather than
Morgane Agostini -
Regarding heteroscedasticity, you noted that using an OLS regression, you found heteroscedasticity, transformed, and still found it. That could be because the transformation did not handle enough of the heteroscedasticity. I don't recommend transformations for that reason, and also for ease of interpretation. There are two kinds of heteroscedasticity in regression: essential heteroscedasticity, which is just a natural result of the difference in size of different predicted-y values, and there is nonessential heteroscedasticity due to model and/or data issues. Remarkably, 'fixing' the nonessential heteroscedasticity should still leave you with the essential heteroscedasticity, and if not, it is model and/or data issues which also could be blamed for NOT having heteroscedasticity.
If you are doing panel data then you may well have autocorrelation as well as heteroscedasticity, and want to look at GLS, generalized least squares regression. But if you are only looking at one time period, say finite population statistics, and spatial autocorrelation is not at issue, then you only need to consider weighted least squares (WLS) regression. Rather than transform, you can model the heteroscedasticity by using the coefficient of heteroscedasticity, gamma, which is related to the regression weight, and figures into regression coefficients. See https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, with various updates in reverse chronological order, and associated papers.
As for the p-value, it is dependent upon sample size and effect size. If you want to check model fit, you had better consider a "graphical residual analysis." To study whether your model fits your sample so closely that it does not do well for the remainder of the population or subpopulation you wish to model, consider "cross-validation." There are other measures, such as "AIC."
You may also consider whether you are interested in prediction or explanation. See Galit Shmueli: https://www.researchgate.net/publication/48178170_To_Explain_or_to_Predict. The example in the appendix may be of interest. Purely for prediction some may suggest considering principal components, but then a chance at any explanation would be rather lost, and I would expect to generally want some interpretation. Note also that explanation only goes so far since there are generally relationships among the predictors, notably collinearity.
For prediction we want the best set of predictors, no more or less, working together to approach the 'ideal' predicted-y. Then Y|predicted-y should 'ideally' have essential heteroscedasticity.
With panel data and a time (autocorrelation) feature, things are more complex, but not my area.
Best wishes - Jim
PS -
Using a graphical residual analysis (you said you used) with and without a particular variable in the model, and a cross-validation in each case, should indicate the value (or lack of it) as part of your model.
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