Bias from classical and other forms of measurement error

We consider the implications of an alternative to the classical measurement-error model, in which the observed, mismeasured data are optimal predictions of the true values, given some information set. In this model, any measurement error is uncorrelated with the reported value and, by necessity, correlated with the true value of interest. In a regression model, such measurement error in the regressor does not lead to bias, whereas measurement error in the dependent variable leads to bias toward 0. In general, the measure ment-error model, together with the information set, is critical for determining the bias in econometric estimates.