Measurement error

Question 1

what are the two types of measurement error?

Answer 1

1. Measurement error in the dependent variable: observe y instead of y∗
   2 Measurement error in an explanatory variable: observe x instead of x∗

Question 2

What are implications for bias and consistency if we have measurement error in DV and the measurement error is uncorrelated with the IV?

Answer 2

As long as measurement error e0 is uncorrelated with the explanatory variable x1, the OLS esimator of β1 is unbiased and consistent.

Question 3

what happens to standard error if we have measurement error in DV and the measurement error is uncorrelated with the IV?

Answer 3

greater variance in the OLS estimator (larger standard errors).

Question 4

what happens to standard error if we have measurement error in IV and measurement error e1 is uncorrelated with the observed measure x1?

Answer 4

larger standard errors

Question 5

classical measurement error

Answer 5

e1 is uncorrelated with the unobserved
measure x1* . This would arise when the observed x1 is the sum of the true explanatory variable and random noise: “classical measurement error”.
Then there is necessarily correlation between x1 and e1

we then have attenuation bias

Question 6

what is attenuation bias?

Answer 6

The estimator is biased toward zero. The amount of bias depends on the variability in x1∗ (signal) versus the variability in e1 (noise).