Hi, I used a WLSMV method to estimate the following model, in which y1 is a binary variable and y2 is a continuous one:
... y1 ON x1 x2 x3 y2 ... y2 ON y1 x1 x2 x4 ...
The reviewer's challenge is that the Pearson's correlation between y1 and x4 is .18 (significant at .05 level) and that between y2 and y4 is -.14 (insignificant at .05 level). So x4 should be included in the first equation too. I think, by doing that, x4 is not an exogeneuous variable any more.
Technically, is the reviewer's challenge correct? If not, could you please recommend one or more references to explain this matter? Thanks a lot!
Seems to me that x4 is still exogenous even if you include it in the y1 equation. Whether x4 should be included there is a substantive-theoretical matter that can then be tested. The fact that the correlation is significant doesn't mean it needs to be there, since x4 should be seen in the context of the other covariates for y1, i.e the regression coefficient is a partial one.