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The Probability Limit of the OLS Estimator in the Case

question 34

Essay

The probability limit of the OLS estimator in the case of omitted variables is given in your text by the following formula: β^1pβ^1+ρXσuσX\hat { \beta } _ { 1 } \stackrel { p } { \rightarrow } \hat { \beta } _ { 1 } + \rho _ { \mathrm { X } } \frac { \sigma _ { u } } { \sigma _ { \mathrm { X } } } Give an intuitive explanation for two conditions under which the bias will be small.


Definitions:

Zygote

The initial cell formed when a sperm cell fertilizes an egg cell, representing the earliest stage in the development of an organism.

Placenta

A vital structure that forms inside the uterus throughout pregnancy, supplying the fetus with oxygen and essential nutrients while eliminating its waste materials.

Fetus

A developing mammal or human from the completion of embryonic development to birth, characterized by rapid growth and the development of body structures.

Embryo

A stage in prenatal development after fertilization and before becoming a fetus, characterized by rapid cell division and the start of cell differentiation.

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