Time dummies - Intuition

Question

Consider a simple two-way fixed effects model: \begin{equation} y_{it}= x_{it} \beta + \alpha_i + \delta_t + u_{it} \end{equation} where $x_{it}$ is a row vector of regressors of size $K$, and $\alpha_i$ denotes the unobservable individual-specific effects, $\delta_t$ denotes the unobservable time effects, and $u_{i,t}$ denotes the stochastic disturbance term.

Can you provide insight into why incorporating time dummies is equivalent to transforming the variables into deviations from time means (i.e., the mean across the $N$ individuals for each period)?

Here is a related answer for the $\alpha_i$, a similar logic applies to time dummies: https://stats.stackexchange.com/questions/174243/difference-between-fixed-effects-dummies-and-fixed-effects-estimator/174267#174267 — Christoph Hanck, Dec 31 '23 at 13:29

score 1 · Accepted Answer · answered Dec 31 '23 at 19:01

1

This should be straight forward. Consider the variable $z_{i, t}$, which are the deviations from the time means. Since these are deviations from the mean, we can write them as

$$ z_{i, t} = y_{i, t} - \delta_t $$

Can you take it from here?

answered Dec 31 '23 at 19:01

Demetri Pananos

36,121

Time dummies - Intuition

1 Answers1