Two-way fixed effects demo

fixed_effects_demo.R

unit_effect = rnorm(5)
time_effect = rnorm(5)

unit = rep(1:5, each = 20)
time = rep(1:5, times = 20)
x = rnorm(100)

y = unit_effect[unit] + time_effect[time] + .5 * x + rnorm(100)
df = data.frame(y = y, unit = factor(unit), time = factor(time), x = x)

fit1 = lm(y ~ unit + time, data = df)
fit2 = lm(y ~ unit + time + x, data = df)
# The two regressions return different fixed effect coefficients-- the fixed
# effect coefficients are no longer means if there are additional predictors.
# Also note the estimate of x's coefficient is accurate.