This question is somehow related to this one and this one.

I have two models with the same independent variables on the same dataset.

Model1: Y1 = alpha0 + alpha1 X1 + alpha2 X2 + error1

Model2: Y2 = beta0 + beta1 X1 + beta2 X2 + error2

These models only differ by their dependent variables Y1 and Y2. Y1 and Y2 are two different measures of risk, and do not have identical scales and distributions. X1 is the variable of interest and X2 represents control variables. Because X1 is endogeneous, I estimate these models with an instrumental variable regression (IV).

I want to know if X1 is better at explaining the cross-sectional variations in Y1 than in Y2.

Can I compare the respective marginal effects of X1 on Y1 and X1 on Y2, and then conclude for instance that X1 has a higher marginal effect than X2?


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