Obviously not - a flat standard deduction by definition gives no tax advantage for having a(nother) child.
Ha! We have 20 years of higher personal exemptions and declining birth rate, but of course that doesn't mean anything.
A multivariate analysis means more.
It sounds like their theses is "increasing the exemption will increase the fertility rate provided all of the other factors driving the rate lower go away."
It sounds like you have no idea what a multivariate analysis is about. Please note that this is not my problem to solve for you.
there will always be other factors
Which means only that the per-child tax credit (no longer an exemption - thanks for reminding me) would have to be increased that much more to counter other variables tending to decrease fertility rates.
You're the one calculating the effect of the exemption/credit.
What other factors did you include in your multivariate analysis that leads you to believe a net $10/month is going to lead to an increase in the fertility rate?
Or didn't you try to model the real world either?