Can anyone point me to a straightforward discussion/derivation of the potential drawbacks of using aggregate proxies (say census tract median income instead of individual income) in place of multiple missing individual socioeconomic independent variables? Assume that the missing individual data cannot be estimated via hot decking or some similar procedure. As I understand it, using even a bad proxy is preferred to not controlling for an important element in the data generating process. Still, I'm sure there are problems with the approach and I would like a clear explanation of what to anticipate, and if possible, how to correct for them.
Any help is highly appreciated!
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