The Errors-In-Variables Model Analyzed in the Text Results In So That the OLS Estimator Is Inconsistent

question 26

Essay

The errors-in-variables model analyzed in the text results in $$\hat { \beta } _ { 1 } \stackrel { p } { \rightarrow } \frac { \sigma _ { X } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } } \beta _ { 1 }$$ so that the OLS estimator is inconsistent.Give a condition involving the variances of X
and w, under which the bias towards zero becomes small.

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Definitions:

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Shortage

An occurrence in which the need for a particular product or service surpasses the available amount in the market.

Binding Price Ceiling

A legally imposed price limit that is set below the equilibrium price, leading to a shortage as demand exceeds supply at that price level.

Graph (a)

A graph is a visual representation of relationships between two or more variables or sets of data, often using lines, bars, or points in a two-dimensional or three-dimensional space.