A somewhat common device in panel data models is to lag explanatory variables when they're suspected as being "endogenous." It often seems to be done without much thought, as if lagging solves the problem and we can move on. I have some thoughts about it.
#metricstotheface
#metricstotheface
First, using lags changes the model -- and it doesn't always make sense. For example, I wouldn't lag inputs in a production function. I wouldn't lag price in a demand or supply function. In other cases, it may make sense to use a lag rather than the contemporaneous variable.
Under reasonable assumptions, the lag, x(i,t-1) is sequential exogenous (predetermined). You are modeling a certain conditional expectation. But, logically, it cannot be strictly exogenous. Therefore, fixed effects estimation is inconsistent with fixed T, N getting large.
However, if the idiosyncratic errors are I(0), the "bias" in FE is on the order of 1/T; it may be acceptable if T is somewhat large. First difference OLS is a disaster as the bias never goes away no matter how large is T.
The alternative is to FD and look into the past for IVs.
The alternative is to FD and look into the past for IVs.
But if one takes this Arellano-Bond approach, you might as well use x(i,t), first difference, and look in the past for IVs.
Better is to find convincing external instruments for the endogenous elements of x(i,t) -- easier said than done.
Better is to find convincing external instruments for the endogenous elements of x(i,t) -- easier said than done.
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