Suppose you have a model which is panel data, which looks like this:

Yit=t+1Xit+it

That is, an observation is an individual (i) at a time (t). Your model, as you can see above, assumes there is a fixed "time effect" for each period. If you had lots of time periods, this would be difficult to estimate, since there would be lots of _t to estimate. You decide on a difference model. Define:

Yit=YitYi(t1)

Xit=XitXi(t1)

it=iti(t1)

You know that E[_it | X_it] = 0 for any t. Find an equation for Y_it in term of the other objects. Suggest how you could find the value of ₁ without estimating all of the time period effects.