Declining birth rate would also reduce demand for labor, not just supply, no? Assuming that the relationship between population and demand for labor is linear (probably isn't, I don't know economics).
I think it's a delayed effect. As the populace ages, people who are retired (from when birthrates were higher) will make up a larger percentage of the total population. There's some existing info on this out there, but most of what I have seen focuses on how this will impact Social Security in the US.