http://adsabs.harvard.edu/abs/1964AmJPh..32...52O American Journal of Physics, Volume 32, Issue 1, pp. 52-55 (1964): "Gravitational redshift of photons from a star and gravitational bending of the path of photons grazing the sun can be derived by using only Newton's laws and the idea of a photon as a particle of mass hv/c^2. The difference between the relativistic and Newtonian equations for gravitational redshift is too small to be detected and, therefore, gravitational redshift does not provide experimental verification of the general theory of relativity."
That is, the shift in frequency is caused by the shift in the speed of light in a gravitational field, as predicted by Newton's emission theory of light. It can be shown that, if the speed of light varies with the gravitational potential as predicted by the emission theory (c'=c(1+gh/c^2)), then, in gravitation-free space, it varies with the speed of the observer again in accordance with the emission theory (c'=c+v):
http://www.youtube.com/watch?v=FJ2SVPahBzg "The light is perceived to be falling in a gravitational field just like a mechanical object would. (...) The change in speed of light with change in height is dc/dh=g/c."
Integrating dc/dh=g/c gives:
c' = c(1 + gh/c^2)
Equivalently, in gravitation-free space where a rocket of length h accelerates with acceleration g, a light signal emitted by the front end will be perceived by an observer at the back end to have a speed:
c' = c(1 + gh/c^2) = c + v
where v is the speed the observer has at the moment of reception of the light relative to the emitter at the moment of emission. Clearly, the speed of light varies with both the gravitational potential and the speed of the observer, just as predicted by Newton's emission theory of light.