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
Yit = β0 + β1Xit + β3St + uit,
Show how β1 can be estimated by the OLS regression using "time-demeaned" variables.