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?

---

Definitions:

C=C Stretching Frequency

Refers to the frequency at which the carbon-carbon double bonds in a molecule vibrate, typically observed in infrared spectroscopy.

IR Absorption

The absorption of infrared radiation by molecules, leading to changes in vibrational energy levels, used in spectroscopy to identify functional groups.

Intense IR Absorption

A characteristic of some materials to strongly absorb infrared radiation at specific wavelengths, indicative of particular molecular bonds.

Characteristic IR Absorption

The specific frequency at which a molecule absorbs infrared light, indicative of particular bonds or functional groups within the molecule.