Consider the Case of Time Fixed Effects Only, I $$Y _ { i t } = \beta _ { 0 } + \beta _ { 1 } X _ { i t } + \beta _ { 3 } S _ { t } + u _ { i t } ,$$

question 17

Essay

Consider the case of time fixed effects only, i.e., $$Y _ { i t } = \beta _ { 0 } + \beta _ { 1 } X _ { i t } + \beta _ { 3 } S _ { t } + u _ { i t } ,$$
First replace $\beta _ { 0 } + \beta _ { 3 } S _ { t }$ with $\phi _ { t }$ . Next show the relationship between the $\phi _ { t }$ and $\delta _ { i }$ in the following equation $$Y _ { i t } = \beta _ { 0 } + \beta _ { 1 } X _ { i t } + \delta _ { 2 } B 2 _ { t } + \ldots + \delta _ { T } B T _ { t } + u _ { i t }$$ 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:

Inventory Valuation

The method used by businesses to assess their inventory's worth at the end of an accounting period, affecting financial statements and tax obligations.

Conservatism

An accounting principle that guides accountants to choose methods and assumptions that are least likely to overstate assets and income.

Distribution Costs

Expenses related to delivering goods from the manufacturer to the end consumer, including transportation and warehousing.

Balance Sheet

A financial statement that provides a snapshot of a company's financial position at a specific time, showing assets, liabilities, and shareholders' equity.