Fixed effects, lagged dependent variables, or what?

Arzu Kibris asks

Question: Suppose you have data on turnout at the county level for two
periods, t and t-1, and suppose there has been a change in the
electoral threshold in some states from t-1 to t. You want to analyze
whether this change has effected turnout. Because counties are
clustered within states, you think there might be some unobserved
state level effects which you control with state dummies. In models of
electoral behavior, to capture habit, lagged dependent variable is
also included as a control. So, in this example turnout at  t-1 is
included as an independent variable. Would such a model be considered
a fixed effects model with lagged dependent variable? It does not
include county-level fixed effects , nonetheless province level fixed
effects are still accounted for. I could not place such models in your
discussion. I would really appreciate if you could clarify.

Interesting question Arzu. First thing I would do to clarify the problem

is focus on the source of variation. If the law changes of interest are

at the state level, then that’s where the action is. You want to control

for state effects since thats the source of OVB. You can control for county

effects but counties are a red herring once you’ve got states under control.

It sounds like you are trying to have both fixed effects and lagged dependent

variables. I don’t find the idea of lagged dependent variables very appealing

in state-level DD. Its hard to see why the lagged dependent variable is a

primary source of OVB, while there are almost surely time-invariant state effects

to worry about.

Good luck with your project!

JA