While panel data bring with them important benefits, standard modeling challenges necessarily lurk. For example, one can estimate fixed-effects models to control for endogeneity, but at the potential cost of forgoing studying time-invariant variables. Alternatively, one could estimate a random-effects model, but introduce potential bias.
When confronting such a trade-off with panel data, my initial default position is to run two separate models (FE and RE) and assess whether any key results are model-specific. However, other empirical strategies have emerged relatively recently. While I am unsure whether similar coding possibilities exist in R, SAS, or SPSS, Stata's correlated random-effects model (CRE) allows one to estimate both time-varying and time-invariant effects while controlling for endogeneity that arises when variables correlate with unobserved panel-level characteristics. That is, CRE models allow researchers to, in essence, "have it both ways at the same time" by controlling for any endogeneity by including the panel means of time-varying variables as additional controls in the model. For a brief introduction and helpful examples and videos, click here, here, and here.
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