In DSGE model, can we directly judge the change of Lagrange multiplier by the change of exogenous shock?

I recently read the article Financial Business Cycles by Iacoviello (2014). In the third paragraph of chapter 2.4on page 10, the author mentions: When the capital adequacy constraint becomes tighter,the banker’s multiplier on the borrowing constraint λB,t gets higher. Since I am still a beginner, it is difficult for me to see directly from the formula given by him how the change of the Lagrange multiplier is affected by these variables and shocks. Can anyone tell me the basis on which the author puts forward this conclusion?
Thanks a lot!

I am not sure I get the point. The Lagrange multiplier on a constraint by construction increases when a constraint becomes tighter (the Lagrange multiplier measures the change in the objective when the constraint tightness marginally changes). It does not matter what the cause of the increasing tightness is to get this result.

Thank you very much for your reply. I want to know why the Lagrangian multiplier on a constraint by constructionmust increase when the constraint becomes tighter, why not decrease? I never seem to know this point of knowledge.

Because the multiplier measures the tightness of the constraint. If it’s zero, the constraint is not binding at all, i.e. slack. See also Shadow price - Wikipedia

Thank you very much!