In my search for research articles to make fun of, I found this one entitled ‘Regressions on skewed variables in accounting and corporate finance’. [1] I didn’t understand the title and I didn’t understand the first sentence. Here it is:
“Many empirical accounting and corporate finance studies estimate OLS regressions on skewed dependent variables, which can produce biased estimates of the economic and statistical significance of the regressors because the mean of a skewed variable is also a function of the skewness parameter that may vary across observations or depend on regressors.”
I have to admit my complete ignorance on every one of the technical terms in the sentence, except for statistical significance and regression. I can’t remember what the initials OLS stand for so I have no idea what an OLS regression could be. I can imagine what a dependent variable is but not a skewed one and certainly not the ‘mean’ of a skewed variable. Regressors defeat me completely as does the skewness parameter, especially one that may vary across observations.
Not having understood the abstract and the first sentence, I went directly to the conclusion of the paper to see if I could glean some understanding. It turned out to be more complicated, because the authors included even more terminology I didn’t understand, especially ‘yield biased estimates of the coefficients and standard errors’, with the introduction of another regression: the quantile regression, and the rather bizarre ‘outliers’.
So, I was lost and bewildered, but I decided to push on and read the rest of the paper.
I was please to find even more statistical expressions I didn’t understand. The one that sounded the best was ‘winsorizing’. It made me think of Winsor castle in the UK, whereas its cousin ‘trimming’ brought back memories, when I used to cut the hedge in my garden. Things became complicated when I learnt that ‘a first-order Taylor series approximation’ induces ‘endogeneity bias’. I have vague recollections of a certain Brook Taylor whose 1715 theorem I discovered and forgot in my calculus lessons at school. The reason given for this bias though was a little depressing, because the words are simple but the meaning less so. The bias arises because the error terms include the higher-order terms.
Reading further, I discovered that OLS means ordinary least squares which merely complicated things further, so I found a pdf manual on Google to explain it. I should have remembered that OLS is the best fitting straight line through a set of data points.
So the authors are saying that OLS regressions do not always work with skewed variables, because they give the wrong results or as they say they ‘produce biased estimates’. It turns out that skewed variables can be almost any financial variable from cash flow and capital expenditure to profitability and leverage. So instead of using OLS regression the authors recommend not one, but several quantile regressions after discarding alternative approaches such as trimming, winsorizing and others. Further, they say, one gets more information on the outliers: the extreme variations in the data set.
So the next time you analyse financial data, don’t automatically assume that OLS regressions will work, but try out the more complicated quantile ones.
[1] Regressions on skewed variables in accounting and corporate finance, on SSRN, March 2025, by Robert Kieschnick, University of Texas at Dallas, Wendy Rotenberg, University of Toronto and Kai-Sheng Song, University of North Texas.