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I am conducting difference-in-differences analysis. The first difference is from time, treatment/control, and the second is from treated subjects, A and B. There are two control variables, ITEM and SIZE. The A and B have one and two ITEMs, respectively. For each ITEM, SIZE divides into three categories. The attached picture is a frequency table of these variables.

enter image description here(ITEM1-3 and SIZE1-12 are dummy variables)

A dependent variable, log price, is obviously affected by ITEM and SIZE. So I want to control these variables, but there is a multicollinearity issue. For instance, SIZE1-3 combined is the same as ITEM1 which is the same as A. To avoid this problem, what I have in mind is to control SIZE2-3, SIZE5-7, SIZE9-12. In other words, I control all SIZE dummy variables but SIZE1, SIZE4, and SIZE8. Is this right specification? Can a D-in-D coefficient capture treatment effect without bias in this specification?

Thank you much in advance.

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The occurrence of multicollinearity does not reduce the predictive power of the model as a whole, though it affects the reliability of the coefficients of individual predictors.

I usually detect Multicollinearity using VIF (Variance inflation factor). So higher the VIF value higher the Multicollinearity. Usually, if we have high VIF value then we can remove it.

But there is a constraint here. If you have very low p-value and high VIF then we can not ignore this variable.

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