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Measuring Measurement Error

Although 2SLS is most often applied to deal with omitted variables or simultaneity, we show that in practice it also resolves a substantial amount of attenuation bias resulting from classical errors in variables. We analyze 398 pairs of OLS and 2SLS regressions in 57 papers published in top economics and finance journals; we find that even when theory suggests the OLS coefficient should be inflated relative to the 2SLS coefficient, the 2SLS coefficient is in fact larger 85% of the time. Classical measurement error, i.e. differences between the underlying economic variables and what is measured by the econometrician, can explain this phenomenon. We derive simple regression specifications to quantify the extent of measurement error and estimate that approximately 23% of the variation in the average instrumented regressor is white noise.