21: Panel Data and Fixed Effects Flashcards
error term in panel data
αi +uit (2 components) - error term as something fixed and time-variant
αi
- fixed effect including all unobserved variables that are constant over time for each unit i
uit
- all the remaining time-unit specific error
issue with error term in panel data
αi is unobserved and contains unit-specific characteristics which could be correlated with regressors
- with OLS, estimates will be biased
FE estimation
subtracts from each side of the equation the average of the corresponding side computed over all observations belonging to the same unit
- disappearance of the fixed effect (αi) which is what we want
cancels out the unobserved unit fixed component that you’re worried about so you can run OLS
when can we use FE estimation?
only for outcomes and explanatory variables that have variation within the unit over time
FE and adding dummies
instead of demeaning all variables, you can include a full set of unit-specific dummy variables
- allows each unit to have a different intercept but same slope
- drop the first dummy to avoid perfect multicollinearity
FE estimator and adding unit-specific dummies yield identical coefficients and standard errors
FD estimation
using panel data to hold unobserved effects constant with only two time periods
differencing out αi so you can estimate the regression with OLS
regressing changes of Y on changes of X so fixed effect doesn’t play a role since by assumption, fixed effect doesn’t change over time
- mean deviation is the change relative to the mean
FE vs. FD
with 2 time periods, FE and FD are the same
with more than 2 time periods, they lead to different estimates
- differently affected by serial correlation of the uit error term (FD based on change of uit while FE is on uit-dash uit)
typically a good idea to estimate and report both
time fixed effects
something common across all units
αt (instead of αi) +uit
- now each time period instead of unit has a separate intercept
two-way FE
if some OVs are constant over time but vary across units while others are constant across units but vary across time, include both unit and time FE
- demeaning the dependent and independent variables twice
running unit-level FE estimation but also including time dummies
random effects estimation
OLS assumes that uit is iid but you might have serial correlation in the error term (αi +uit) if you don’t difference away αi
random effects estimates αi and point estimates on dummies
- only good when correlation of the error term is 0
deals with serial correlation but not identification
FE estimation and DiD
with two-way FE, can write the same DiD regression but with no dummies and just intercepts
two-way FE as the most common way to implement DiD estimation strategy where the basic idea is identifying the effect of X on Y without confounding things in the error (both unit and time-specific)
