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