From Classical and Other Forms of Measurement Error 481

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 measurement-error model, together with the information set, is critical for determining the bias in econometric estimates. KEY WORDS: Classical measurement error; Optimal prediction error; Regression analysis. Many variables used in econometric analyses are recorded with error. These errors may have occurred at various stages of the data collection. They may be the result of misreporting by subjects, miscoding by the collectors of the data, or incorrect transformation from initial reports into a form ready for anal-ysis. Often such errors are ignored. In cases in which explicit attention is paid to measurement error, it is typically assumed to be “classical measurement error, ” in which the error is inde-pendent, or at least uncorrelated with, the true value of th