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

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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.

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Definitions:

Treaty of Prague

An agreement concluded in 1866 after the Austro-Prussian War, leading to the dissolution of the German Confederation and the establishment of the North German Confederation.

Ausgleich

The compromise of 1867 that established the dual monarchy of Austria-Hungary.

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