I always hesitate to write this lest I open myself up to parody, but I think "empirical evidence" is one of the most overrated things in policy debates. There are compelling theoretical reasons to believe that, ceteris paribus, if the tax-and-transfer system subsidizes families with children that people will have more children. Kevin Drum rebuts this with the observation that fertility rates are poorly correlated with the real value of the per child tax subsidy:
I buy it, but on another level I don't buy it at all. This is just a chart showing that we've had sweeping waves of social and economic trends over the decades that totally swamp tweaks in the tax code. It's true that you can put together a two-variable chart with appropriately-scaled axes to make it appear silly to say that the tax code is having an influence on fertility rates, but really the chart tells us nothing. We know that some people have children, and that different people have different numbers of children. We know that people exercise some level of conscious choice about this. And we know that having children is costly in both financial and nonfinancial ways. People also find it rewarding. But the costs are real and extra money to defray those costs should, at the margin, encourage people to have more children. I'd say the most important issue here is that not only do women have more educational and labor market opportunities these days, but there's extremely sluggish "productivity growth" in the "pregnancy sector" so in effect it's becoming more and more costly to actually do the work of having a child.
That's not to say their are no empirical issues here. If you want to use public funds to boost fertility rates you'll want to know how best to target those funds. That is a difficult empirical question that I think it would be hard to design rigorous studies of, but such studies might be very useful.