3Panel Data.pdf

Recitation Notes 3
Konrad Menzel
September 30, 2006
1 Estimation with Panel Data
Basic Setup
Suppose we want to estimate the intertemporal elasticity of labor supply. Under certainty about future
prices
hit = hit(pit, wit, λit)
where λi is the worker’s marginal utility of wealth, which corresponds to the Lagrange multiplier from
the UMP. Since without uncertainty and borrowing constraints, the individual sets up his lifetime con­
sumption plan once and for all facing a single life-time budget constraint, optimality of that plan requires
1
that λit = λi doesn’t change over time, which means that λi summarizes all the information about all
other periods in the optimization problem which is relevant to determine demands in period t.
Under the right functional form assumptions (among others separability within and across periods), the
corresponding estimation problem has the following structure
hit = witβ+ αi + εit
where hit is log hours worked, wit is log wages in period t, and αi is a function only of the Lagrange
multiplier λi and preference parameters which are constant over time. What will happen if we just pool
all the data and run OLS? Well, the new model now is
log(h ) = w β+ [α−α] + ε
it it i it
=: ηit
1 N
(where α:= N i=1 αi). From this we can see that there are two reasons why the Gauss-Markov
assumptions (on th