The best replacement for fixed effects is random effects.

The best alternatives to fixed effects are rated as following:

★★★★★	random effects
★	first difference
★	difference in difference
★	pooled ols
★	mixed effects
★	first differencing
★	clustered standard errors
★	first differences
	clustering
	dummy variables
	pooled
	ols

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Speaking about fixed effects, one probably shouldn't forget about clustered standard errors.

Other search terms related to fixed effects and their ratings are:

★★★★★	clustered standard errors
★★★	lagged dependent variables
★★	stata
★★	instrumental variables
★	panel data
	logit
	probit

You have in mind a companion for fixed effects and it is not yet here? Propose!

Google Trends

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fixed effects

random effects

first difference