Your Textbook Suggests an "Entity-Demeaned" Procedure to Avoid Having to Specify

Essay

Your textbook suggests an "entity-demeaned" procedure to avoid having to specify a potentially large number of binary variables. While it is somewhat tedious to specify a binary variable for each entity, this can still be handled relatively easily in the case of the 48 contiguous states. Give a few examples where it might be close to impossible to implement specifying such large number of entity binary variables. The idea of the "entity-demeaned" procedure was introduced as a computationally convenient and simplifying procedure. Since there are also time fixed effects, why is there no discussion of using a "time-demeaned" procedure? Using the following equation
Y_it = β₀ + β₁X_it + β₃S_t + u_it,
Show how β₁ can be estimated by the OLS regression using "time-demeaned" variables.