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 $$Y _ { i t } = \beta _ { 0 } + \beta _ { 1 } X _ { i t } + \beta _ { 3 } S _ { t } + u _ { i t } ,$$ $$\text { Show how } \beta _ { 1 } \text { can be estimated by the OLS regression using "time-demeaned" variables. }$$