Comparing two models with different dependent variables after an IV regression

[Bertrand Groslambert]

Dear Stata users,

I have two models with the same independant 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).

Q1: Is it righ to compare the adjusted R-square in order to state that Model1 has more explanatory power than Model2 (assuming higher R-square for Model1)?

Q2: Is it right to 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?

Q3: Based on Q1 and Q2, can we say that X1 is better at explaining the cross-sectional variations in Y1 than in Y2?

Many thanks.

Bertrand

Stata13

[Bertrand Groslambert]

My question is somewhat related to this thread but I don't think the answer of using Seemingly Unrelated Regression -sureg- applies as I work with Instrumental Variables.

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

1. If you must compare fit, AIC and BIC are preferred.
2. While you can compare the parameters across equations, it is not clear that it is meaningful. The marginal effects will depend on the scaling of the y's so rescaling one of the y's will change the results. They're influencing different things so comparing influence is questionable.
3. I guess you can, although this is questionable.

[Bertrand Groslambert]

Phil Bromiley: Thanks for your answer.

This is a general question about comparing regressions and not an issue about coding.

My understanding is that we cannot use AIC or BIC if dependent variables are not the same.