Fixed time effects or fixed individual effects?

I have the following question or problem. I am currently using panel data to predict the hourly wage. I have only used the variable "union" as an influence variable from the initial model, but I assume an overestimation (Model 1). For this reason, I have now also included the variables educ and exp, but the coefficient of union has only changed slightly (Model 2). Since I have panel data, it makes sense to consider fixed effects. In model 3 I have included fixed time effects, but the coefficient has still hardly changed (model 3). But if I now include fixed individual effects, then it changes significantly, it almost halves (model 4). Now to the question. How do I know if fixed time or fixed individual effects make more sense? I would say purely intuitively that the consideration of fixed individual effects make more sense, because there the coefficient changes significantly more, but I am not sure? Which modeling would you prefer? Model 3 or Model 4? And why?

This is my code:

reg lnwage union, r *Model1
reg lnwage union exp educ, r * Model2
reg lnwage union exp educ i.year, r * Model3
xtreg lnwage union exp educ i.year, fe r *Model4


This is my output:

Typically, you use both time and individual FE's. Recommended reading- Mostly Harmless Econometrics's setup for panel data Difference-in-Differences (DiD). You may not have a good DiD setup, but it is there nominally, at least.

I note something's wrong - a sort of multicolinearity is present and problematic since you have dropped EDU.

• Thank you. And if you had to choose one of the models? I think that in the first regression the effect of "union" is overestimated, mainly because of unobservable influences. Since taking into account time effects (3) does not change the coefficient much, but individual fixed effects do, I would prefer model (4). Do you agree? Jun 19, 2022 at 6:51
• I don't think I can endorse anything without a lot more context than can be provided over a post. Think a full complete draft of a paper for an "endorsement". However, one would expect both time FE and individual FE for most purposes, which is your last model. But - there's still something happening that is dropping EDU. Jun 19, 2022 at 15:11

As RegressForward says, typically it’s good practice to include both time and individual FEs.

If one or both matter depends on whether and to what degree observations are correlated within individuals across years and/or correlated across individuals within years. Understanding the data is crucial to assess this.

As a rough guess, it looks like you have a large N + short T panel, so lots of individuals and presumably your variables are quite persistent within an individual over time (wage, edu, etc are pretty persistent). This would imply that observations in the panel of the same individual over time are correlated. And this suggests that individual FEs are important to include and explains why including them impacts your coefficient on Union, which itself may also be persistent within individuals.

Also is the edu variable constant within each individual? If so, it’d be confounded with the individual FE hence it drops out of the regression.