Here is how an empirical model (Einstein's general relativity) works:

The gravitational redshift is produced by the variation of the speed of light predicted by Newton's emission theory of light, so any measurement of the gravitational redshift directly confirms this variation:

"If we accept the principle of equivalence, we must also accept that light falls in a gravitational field with the same acceleration as material bodies." http://sethi.lamar.edu/bahrim-cristi...t-lens_PPT.pdf

University of Illinois at Urbana-Champaign: "Consider a falling object. ITS SPEED INCREASES AS IT IS FALLING. Hence, if we were to associate a frequency with that object the frequency should increase accordingly as it falls to earth. Because of the equivalence between gravitational and inertial mass, WE SHOULD OBSERVE THE SAME EFFECT FOR LIGHT. So lets shine a light beam from the top of a very tall building. If we can measure the frequency shift as the light beam descends the building, we should be able to discern how gravity affects a falling light beam. This was done by Pound and Rebka in 1960. They shone a light from the top of the Jefferson tower at Harvard and measured the frequency shift. The frequency shift was tiny but in agreement with the theoretical prediction. Consider a light beam that is travelling away from a gravitational field. Its frequency should shift to lower values. This is known as the gravitational red shift of light." https://courses.physics.illinois.edu...re13/L13r.html

Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. [...] The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..." http://www.einstein-online.info/spot...t_white_dwarfs

R. V. Pound and J. L. Snider, Effect of Gravity on Gamma Radiation: "It is not our purpose here to enter into the many-sided discussion of the relationship between the effect under study and general relativity or energy conservation. It is to be noted that no strictly relativistic concepts are involved and the description of the effect as an "apparent weight" of photons is suggestive. The velocity difference predicted is identical to that which a material object would acquire in free fall for a time equal to the time of flight." http://virgo.lal.in2p3.fr/NPAC/relat...iers/pound.pdf

In general relativity measurements of the gravitational redshift should confirm the miraculous gravitational time dilation (fabricated by Einstein in 1911), not the variation of the speed of light. This automatically converts the variation of the speed of light into a fudge factor - irrespectively of the physical plausibility, the variation formula will be anything that makes the gravitational redshift and the gravitational time dilation compatible.

The gravitational time dilation and the gravitational redshift are only compatible if light in a gravitational field behaves in an idiotic way: Its speed DECREASES as the light falls towards the source of gravity - the acceleration of falling photons is NEGATIVE (in the gravitational field of the Earth it is -2g). The idiotic negative acceleration of photons, -2g, was the fudge factor Einstein and his mathematical friends had to introduce in 1915:

Albert Einstein: "Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable." https://archive.is/wn4PV

"The change in speed of light with change in height is dc/dh=g/c." https://www.youtube.com/watch?v=FJ2SVPahBzg

"Contrary to intuition, the speed of light (properly defined) decreases as the black hole is approached." http://www.physlink.com/Education/AskExperts/ae13.cfm

"Einstein wrote this paper in 1911 in German. [...] ...you will find in section 3 of that paper Einstein's derivation of the variable speed of light in a gravitational potential, eqn (3). The result is: c'=c0(1+φ/c^2) where φ is the gravitational potential relative to the point where the speed of light c0 is measured. Simply put: Light appears to travel slower in stronger gravitational fields (near bigger mass). [...] You can find a more sophisticated derivation later by Einstein (1955) from the full theory of general relativity in the weak field approximation. [...] Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911." http://www.speed-light.info/speed_of_light_variable.htm

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