Your Professor Wants to Measure the Class's Knowledge of Econometrics $$\widetilde { X _ { i } ^ { 1 } } = X _ { i } ^ { 1 } + w _ { i } ^ { 1 } ,$$

question 15

Essay

Your professor wants to measure the class's knowledge of econometrics twice during the
semester, once in a midterm and once in a final.Assume that your performance, and that
of your peers, on the day of your midterm exam only measure knowledge imperfectly and
with an error, $$\widetilde { X _ { i } ^ { 1 } } = X _ { i } ^ { 1 } + w _ { i } ^ { 1 } ,$$
where $\widetilde { X }$ is your exam grade, $X$ is underlying econometrics knowledge, and $w$ is a random error with mean zero and variance $\sigma _ { w } ^ { 2 } . w$ may depend on whether you have a headache that day, whether or not the questions you had prepared for appeared on the exam, your mood, etc. A similar situation holds for the final, which is exam two: $\widetilde { X _ { i } ^ { 2 } } = X _ { i } ^ { 2 } + w _ { i } ^ { 2 }$ . What would happen if you ran a regression of grades received by students in the final on midterm grades?

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Definitions:

Principal

The initial sum of money that is invested or lent, used as the foundation for calculating interest and returns.

Assignor

An individual or entity that transfers the rights or interests of a contract to another party, known as the assignee.

Assignee

A party or person who receives rights or interests from another, referred to as the assignor.

Delegator

An individual or entity that assigns responsibility or authority to another party to carry out specific activities or tasks.