From David Card, Ciprian Domnisoru, and Lowell Taylor, the last few sentences are the most interesting:
We use 1940 Census data to study the intergenerational transmission of human capital for children born in the 1920s and educated during an era of expanding but unequally distributed public school resources. Looking at the gains in educational attainment between parents and children, we document lower average mobility rates for blacks than whites, but wide variation across states and counties for both races. We show that schooling choices of white children were highly responsive to the quality of local schools, with bigger effects for the children of less-educated parents. We then narrow our focus to black families in the South, where state-wide minimum teacher salary laws created sharp differences in teacher wages between adjacent counties. These differences had large impacts on schooling attainment, suggesting an important causal role for school quality in mediating upward mobility.
This result is not logically inconsistent with the signalling model, but I think it fits more readily into the human capital story. If you think employers cannot easily distinguish between different qualities of worker (without the educational signal, that is), probably you also should think employers cannot distinguish among the quality of adjacent schools on the basis of what they pay their teachers in relative terms. And in that case, the schools hiring the better teachers are probably increasing the productivity of their students.
For the pointer I thank the excellent Samir Varma.