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I have a question concerning fixed effects regression models. I have a cross-sectional data set which only accounts for one year (2017). I want to look at the effect of one individual factor (e.g., gender) on another individual factor (e.g., perception of economy), wheareas those individuals are nested within different countries.

Is it still possible to run a fixed effects model, or does one always need at least $T=2$ time points? And, does it make sense to use fixed effects, since both variables are on the individual level?

Thank you very much in advance for your answer.

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  • $\begingroup$ Welcome. So you have a cross-sectional dataset from one year and it is comprised of multiple individuals embedded within a series of countries? $\endgroup$ Commented Nov 17, 2020 at 6:04

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You can surely have other fixed effects than unit fixed effects over several time periods.

For example (just one that comes to my mind, there are many others), Geronimus and Korenman, Quarterly Journal of Economics 1992, study the effect of teenage births on economic outcomes such as income relative to needs, \begin{eqnarray*} \log(\text{income/needs}_{fs})&=&\beta_0+\delta_0\text{sister2}_{s}+\beta_1\text{teenbirth}_{fs}\\ &&\quad+\beta_2\text{age}_{fs}+\text{other factors}+a_f+u_{fs}, \end{eqnarray*} To account for socioeconomic effects, they include family specific effects $a_f$, which they can do because they have data for several sisters of one family.

If however, you have $n$ observations, $K$ regressors and additionally want to include $n$ observation specific intercepts, that will not work (with an OLS approach), as you will need to fit $K+n$ coefficients to just $n$ observations.

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If you have individuals nested within countries, then it seems to me you need a mixed-effect model, or a multilevel model, because otherwise you will violate the assumption that the errors are uncorrelated with the dependent variable.

This topic is, I think, very confusing, but Wikipedia has a relatively clear section:

There are two commo assumptions made about the individual specific effect: the random effects assumption and the fixed effects assumption. The random effects assumption is that the individual-specific effects are uncorrelated with the independent variables. The fixed effect assumption is that the individual-specific effects are correlated with the independent variables. If the random effects assumption holds, the random effects estimator is more efficient than the fixed effects estimator. However, if this assumption does not hold, the random effects estimator is not consistent.

This makes it (relatively) clear that the random effects model is to be preferred if the assumption holds.

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