In my nonexperimental data, when running regression, I faced the Simpson Paradox. Simplistically speaking, Pearl,2014 said:
Simpson’s paradox refers to a phenomena whereby the association between a pair of variables (X, Y ) reverses sign upon conditioning of a third variable, Z, regardless of the value taken by Z.
I use the sample of this topic to describe:
You run a linear regression with four numeric predictors (IV1, ..., IV4)
When only IV1 is included as a predictor the standardised beta is +.20
When you also include IV2 to IV4 the sign of the standardised regression coefficient of IV1 flips to -.25 (i.e., it's become negative).
In my case, I use OLS to run the panel data, my method is:
inventory_turnover = b1pt + b2firmsize + b3lnGDP .
pt is a binary variable, representing for treatment group. When I run this regression using fixed-effect model (controlled for firm and year), b1 is positive. But when I add another variable called gross margin to the independent groups (because Gaur,2005 said that gross margin affects inventory turnover), b1 become negative I have a look through the comments and have not found any approach or instruction to deal with Simpson Paradox in linear regression with nonexperimental data.
I am wondering if there is any way to deal with this problem, for example, spotting multicollinearity,... I saw a comment in this topic mention about the residualization approach but I do not know how to spot the variable IV1 in this case.