Under the classical errors-in-variables (CEV) assumption, the measurement error means that the estimated OLS effect, on average, is closer to zero than the true effect.

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CEV assumes that the measurement error is independent of the true value of the variable, which leads to attenuation bias in OLS estimation. This means that the estimated effect is biased towards zero, making it closer to zero on average than the true effect.

Under the Classical Errors-In-Variables (CEV) Assumption, the Measurement Error Means