I have the following regression model R=a+bX+cZX where R is the return and X is a control variable and Z is the variable of interest.

As an alternative approach to the use OLS, often conditional sorts with a construction of portfolios are used. For example, first sort by the control variable and construct e. g. decile portfolios. Second, within these portfolios, sort by the variable of interest and construct e. g. decile portfolios again. Then, portfolio returns can be compared (e. g. whether they are ascending or descending,...)

My question now is whether this method is only allowed if there is no interaction term between the control variable and the variable of interest. In other words, is it allowed to apply the conditional sorting on the regression equation above?


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