199 Measurement Error 6 Measurement error in X (mathematical derivation)

This video mathematically proves how measurement error in a regressor causes the estimated slope coefficient to shrink towards zero. We start with the true model and the observed data, defining the assumptions of classical measurement error. The derivation involves expanding the OLS estimator for the slope and substituting the true model with measurement error. This reveals that the numerator of the estimator is unaffected, while the denominator is inflated by the variance of the measurement error. The resulting fraction, known as the attenuation factor, quantifies exactly how much the estimated slope is biased downwards. Understanding this factor is crucial for interpreting econometric results when measurement error is present. Visit AxiomTutoring.com and subscribe to @AxiomTutoringCourses.