If the cost of living adjustment were “perfect” then it wouldn’t encourage employees to live in any particular place, right? Presumably the whole point is to give each employee the same “effective compensation” for their particular place of residence. Of course, it’s not so easy to agree on what the ideal method of cost of living adjustment would be.
A "perfect" CoL adjustment can't exist. If it's fairly applied across distinct individuals then it won't be perfect for some of them, and if it's applied consistently to a fixed individual that person has enough tweakable parameters to warp the situation to their advantage and actually prefer one location over another. E.g.:
(1) Bob is optimizing long-term savings, and Joe is optimizing purchasing power for nearby activities like bars and restaurants. After subtracting other comparable expenses, any salary surplus strategy which is a "perfect" cross-city CoL adjustment for Bob will when applied to Joe cause him to prefer a cheaper CoL location because his dollars will go further. Supposing the employer doesn't have power to discriminate based on such preferences, no fair CoL adjustment is perfect for both individuals.
(2) Bob is still optimizing long-term savings. MegaCorp chose a "perfect" CoL adjustment based on Bob's preferred standard of living, but the multiplicative nature of price increases in a high CoL city means that Bob can save a ton of money with a mild decrease in his standard of living. He's incentivized to live somewhere more expensive because doing so will maximize his potential savings with minimal impact elsewhere in his life. If the employer isn't discriminating based on what's paid for rent and other expenses, the CoL adjustment is gameable.
The thing is that even if the cost of living adjustment was perfect, that still incentivizes living in a high cost of living area.
It's much easier to move from an expensive city to an inexpensive city than vice versa since your savings will go much further in the inexpensive city.
