First difference estimation with time dummy I am using a first difference estimator for my panel data. The panel has people whom I observe over time. I want to include a 'time fixed effect'. I argue that this should be possible, as long as I interpret it slightly differently than a standard time dummy.
So basically:
 y_it-y_it-1=gamma_(t,t-1)+beta*(x_it-x_it-1)+(e_it-e_it-1)

Where i is a subscript for the crosssectional element and t is the subscript for the time element. 
gamma_(t,t-1) would therefore be a time fixed effect (i.e. dummy variable indicating time) 
A referee claims it is non-sensical. While disagreeing with a referee is a bad idea, I am curious whether he is right or not.
Can someone explain his point ?
 A: Your language is not completely clear here: so it's difficult to agree straight away that the reviewer disagrees with the approach rather than its application or any related claims you make about the model.
If you say that you adjust for a "time fixed effect" you mean to say that, in the statistical model, you have included time or some transformation of time as a covariate. This is not a "first difference estimator" to the best of my knowledge, but I'm unsure what even that would mean.
Whether it is sensical depends on the context of the problem. The reviewer may indeed be wrong. Adjusting for a linear time term is actually the same as accounting for AR-1 auto-correlation. A downside is that such a term makes the assumption that the rate of growth is approximately linear, which can be difficult to grasp if the design is imbalanced, with visits occurring at highly varying time intervals.
For predicting outcomes, fixed time effects are highly prone to extrapolation, especially with polynomial trends.
