Should we avoid overfitting when developing a explanatory (inferential) statistical model? I am planning to conduct a path analysis to figure out the effect from X to Y. (not causality) 
I personally believe that most statistical models should not be overfitted. Whether developing a predictive or explanatory model, overfitting should be avoided. Otherwise, the estimated parameters are not trustworthy. 
However, some research paper or my laboratory member do not pay attention to this. He says that he does not consider overfitting when he fits a linear model for interpretation.
Is my idea wrong? 
I hope someone gives me a comment or resource for these. 
 A: Overfitting is predominantly an issue when building predictive models in which the goal is application to data not used to build the model itself. By definition, when the model overfits to the data that was used to create it, the generalization error of the model goes up.
As far as other applications that are not predictive, overfitting is more secondary, (although if there is no significance attached to included independent variables, you may want to look at transforming certain variables or including additional variables). It's nice when the data and the model aligns- if you have the right experiment design, you can make the argument that the variables you have included are related directly to the variation explained in your model. But far more important are things like interpretability and the fulfillment of the basic assumptions your model may make. It's why some econometricians can suffer a relatively low R^2, particularly if their model is able to show a meaningful connection between independent and dependent variables.
