Consider the case of time fixed effects only, i.e., Yit = 0 + 1Xit + 3St + uit, First replace 0 + ...

Answer: Yit = 1Xit + t + uit. The relationship is 1 = 0, and t = 0 + t for t  2. Consider time period t, then the population regression line for that period is t + 1Xit, with 1 being the same for all time periods, but the intercept varying from time period to time period. The variation of the intercept comes from factors which are common to all entities in a given time period, i.e., the St. The same role is played by 2,  T, since B2t BTt are only different from zero during one period. There is perfect multicollinearity if one of the regressors can be expressed as a linear combination of the other regressors. Define B0t as a variable that equals one for all period. In that case, the previous regression can be rewritten as

Yit = 0 B0t + 1Xit + 2B2t + ... + TBTt + uit.

Adding B1 with a coefficient here results in

Yit = 0 B0t + 1Xit + 1B1t + 2B2t ... + TBTt + uit.

But B0t = B1t + B2t + ... + BTt, and hence there is perfect multicollinearity. Intuitively, whenever any one of the binary variable equals one in a given period, so does the constant. Hence the coefficient of that variable cannot pick up a separate effect from the data. Dropping the intercept from the regression eliminates the problem.

Thank you so much