13.19 Measurement error

• often happens when using proxies
• other possibility: actual measurement error
• \(X = X^* + \epsilon\)

Classical measurement error

• error term is unrelated to latent variable
• leads to attenuation (\(\hat{\beta_1}\) closer to 0 than true \(\beta_1\))
• just treat estimate as lower bound
• if measurement error in \(Y\): no problem, just more stuff in error term

Non-classical measurement error

• error term is related to latent variable
• e.g. self-reported exercising
• real issue!
• addressing this
• Deming regression / Total Least Squares
• GMM
• instrumental variables: use one measurement as instrument for other measurement