# Comparing regression coefficients between models with dependent predictors and dependent criterions

I would like to compare regression coefficients between two models as part of a within-subject study setup. The problem is that both the predictors and criterions are likely to be correlated and that my understanding of repeated measurement analysis is thus far limited.

Basically, I know (from theoretical considerations) that there exists a linear relationship: $$DV_{ij}=\beta_0 + \beta_{1j}IV_{ij}+\epsilon_{ij}$$ where $$i \in 1,..,400$$ (subjects) and $$j \in 1,2$$ (conditions).

I measure both variables two times (2 conditions): $$DV_{i1}, DV_{i2}$$ and $$IV_{i1}, IV_{i2}$$. I expect the variables' values to change.

I want to test whether $$\beta_{11} \ge \beta_{12}$$.

I was thinking about using dummy coding to describe it as an interaction effect as described in this question and I thought about using SUR as described in this question, yet I believe that both approaches would not acknowledge the correlation between the criterions. Likely, my biggest problem right now is that I have too little knowledge about regression and I do not know what to call this "statistical problem" and which "tools" to look for.

I appreciate any remarks and comments.