Consider the Case of Time Fixed Effects Only,i

question 34

Essay

Consider the case of time fixed effects only,i.e. ,
Yit = β0 + β1Xit + β3St + uit,
First replace β0 + β3St with φt.Next show the relationship between the φt and δt in the following equation
Yit = β0 + β1Xit + δ2B2t + ...+ δTBTt + uit,
where each of the binary variables B2,…,BT indicates a different time period.Explain in words why the two equations are the same.Finally show why there is perfect multicollinearity if you add another binary variable B1.What is the intuition behind the fact that the OLS estimator does not exist in this case? Would that also be the case if you dropped the intercept?

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Definitions:

Viruses

Microscopic infectious agents that can only reproduce inside living cells, causing a range of diseases in humans, animals, and plants.

Lymphocytes

The white blood cells—including B cells and T cells—that are the key components of the immune system.

Antibodies

Proteins produced by the immune system to neutralize or destroy pathogens such as bacteria and viruses.

T-Cells

T-Cells are a type of white blood cell that play a critical role in the immune system, helping to protect the body from infection and disease.