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

question 48

Essay

The errors-in-variables model analyzed in the text results in $\hat { \beta } _ { 1 } \stackrel { p } { \longrightarrow } \frac { \sigma _ { X } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } } \beta _ { 1 }$ 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:

Variance

A measure of the dispersion of a set of data points around their mean, indicating how spread out the data points are.

Standard Deviation

A measure of the dispersion or variability of a set of data points, indicating how spread out the values are from the mean of the data set.

Biased Estimates

Estimates that are systematically off-target in a certain direction due to errors in methodology or sample selection.

Absolute Value

The non-negative value of a number without regard to its sign; for example, the absolute value of both -5 and 5 is 5.