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:

Cash Flows

The sum of funds flowing in and out of a company, particularly influencing its ability to cover short-term obligations.

Selling Price

The cost at which a service or item is sold to purchasers.

Required Rate of Return

The minimum annual percentage earned by an investment that will induce individuals or companies to put money into a particular security or project.

Dividend Yield

A financial ratio that indicates how much a company pays out in dividends each year relative to its share price.