(Requires Matrix Algebra)Consider the Time and Entity Fixed Effect Model

question 30

Essay

(Requires Matrix Algebra)Consider the time and entity fixed effect model with a single explanatory variable
Yit = β0 + β1Xit + D2i + ...+ Dni + δ2B2t + ...+ δTBTt + uit,
For the case of n = 4 and T = 3,write this model in the form Y = Xβ + U,where,in general,
Y = ,U = ,X = = ,and β = How would the X matrix change if you added two binary variables,D1 and B1? Demonstrate that in this case the columns of the X matrix are not independent.Finally show that elimination of one of the two variables is not sufficient to get rid of the multicollinearity problem.In terms of the OLS estimator, = ( X)-1 Y,why does perfect multicollinearity create a problem?

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Definitions:

Effectively Control

Effectively control in financial terms refers to the power to direct the financial and operational policies of an entity so as to gain benefits from its activities, often achieved through ownership, contracts, or other means.

Minimum Total Price

The lowest possible aggregate amount that can be charged or paid for a particular set of goods or services.

Pre-Merger Value

The valuation of a company before it enters into a merger or acquisition, often used to assess the financial impact of the merger.

Additional Value

The extra worth created by an investment, project, or action beyond the initial cost or investment.