I estimate the following linear regression model:
yit = αi + δit + γt +
k=t−entry
λkdk
it + xitβ + ηeit
+ f(sit, cit, τ) + εit (1)
where yit is the outcome of interest (i.e., quarterly earnings,
probability of employment) for individual i in quarter t. The
first three terms in Eq. (1) account for unobservable individual
and period-specific factors that affect labor market
outcomes: αi is an individual fixed effect that controls for
time-invariant, person-specific unobservable qualities, such
as ability or motivation, δit allows for individual-specific linear
trends in outcomes, and αt is a quarter-specific fixed effect
that controls for aggregate shocks that affect all individuals
in a given period. The fourth term allows for labor
market outcomes to vary in the quarters before and after welfare
entry, with dk
it indicating whether the current period is k
quarters before or after entry. xit is a vector of time-varying
observable individual characteristics, including a quadratic
term in age (allowed to vary by race/ethnicity), number of
children, age of youngest child, vehicle ownership, and indicators
for months of lifetime welfare receipt (0 months,
1 to 12, 13 to 24, 25 to 59, and 60 or more months).