Hello I have a question about instrument validity in Heckman's selection model. For this purpose, I use the example from Stata itself

Code:
webuse womenwk
heckman wage educ age, select(married children educ age)
Running the above gives us that married and children (as instruments) affect selection into the labor market.

My question is if I run an OLS with wage as the dependent variable, and use all variables as independent variables, then I also get the result that # of children is negatively correlated with wages. Is that a problem? In other words, my concern is that the instrument "children" is directly correlated with wages and not just with selection.

Code:
reg wage educ age married children
Thanks