Consider the Case of Time Fixed Effects Only, I

question 10

Essay

Consider the case of time fixed effects only, i.e.,
Y_it = β₀ + β₁X_it + β₃S_t + u_it,
First replace β₀ + β₃S_t with φ_t. Next show the relationship between the φ_t and δ_t in the following equation
Y_it = β₀ + β₁X_it + δ₂B2_t + ... + δ_TBT_t + u_it,
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:

EBIT

Earnings Before Interest and Taxes, a measure of a firm’s profit that includes all expenses except interest and income tax expenses.

FCFF

Free Cash Flow to the Firm, a measure of a company's financial flexibility that represents the amount of cash generated by a company that is available for distribution among all its security holders.

Tax Bracket

Categories of income tax rates that increase progressively with the amount of taxable income.

FCFE

Free Cash Flow to Equity (FCFE) is the amount of cash available to the equity shareholders of a company after all expenses, reinvestment, and debt payments have been made.