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:

Inherited

The transfer of physical, genetic, or characteristic traits from parents to offspring through genes.

Innate

Qualities, abilities, or knowledge that are inborn or present naturally rather than acquired.

School

A school is an institution designed for the instruction and education of students under the direction of teachers.

Stable Organization

An organization characterized by consistency, resilience, and reliability in its operations, structure, and management, leading to sustained performance over time.