Bounding Parameter Estimates with Nonclassical Measurement Error

Errors in self-reported earnings: The role of previous earnings volatility and individual characteristics

“…If β b 0, then the signs would go in the opposite direction. 14 Black et al (2000) call this assumption a "weak restriction" and it appears to hold in a number of different data sets. Bound and Krueger (1991) find evidence for this in both years (1977 and 1978) of their final, truncated data set for their matched Current Population Survey and Social Security payroll data set.…”

“…However, when measurement error is not classical and the data exhibits mean reversion (σ X Ã , b 0) then the IV estimator will be biased upward. As Black et al (2000) notes, the IV coefficients may therefore serve as an upper bound of the true coefficient when there is non-classical measurement error. 16 As a result, in the presence of non-classical measurement error having a valid instrument does not result in an unbiased estimate of the true population regression coefficient if the mean reversion is strong.…”

“…In this section, I investigate the extent of the bias from using errorridden variables in a bivariate regression (of continuous variables) and discuss how coefficients from an instrumental variables regression may serve as an upper bound on the true effect (see Black et al, 2000 for a thorough discussion of measurement errors in binary, discrete and continuous variables). It is instructive to first identify how the various covariances and variances affect the estimated regression coefficients in the presence of both classical and nonclassical measurement errors.…”

Improving consumption measurement and other survey data through CAPI: Evidence from a randomized experiment

“…When an explanatory variable has such error, its coefficient may be biased either toward or away from zero (Gibson and Kim, 2007). Moreover, the main correction for measurement error bias -instrumental variables (IV) -is inconsistent when errors are correlated with true values (Black et al, 2000).…”

The effect of reporting errors on the cross-country relationship between inequality and crime

“…Such errors are not amenable to standard treatments like fixed effects and instrumental variables. Other methods such as reverse regression and bias bounds (Black et al, 2000) may have greater efficacy, which is a topic for further research. In the absence of these appropriate treatments, the measurement errors in reported crime data are likely to attenuate estimated correlations between inequality and crime.…”