Recent evidence from Bound, Brown, and Mathiowetz (2001) and Black, Sanders, and Taylor (2003) suggests that reporting errors in survey data routinely violate all of the classical measurement error assumptions. The econometrics literature has not considered the consequences of fully arbitrary measurement error for identification of regression coefficients. This paper highlights the severity of the identification problem given the presence of even infrequent arbitrary errors in a binary regressor. In the empirical component, health insurance misclassification rates of less than 1.3% generate double-digit percentage point ranges of uncertainty about the variable's true marginal effect on the use of health services. (c) 2010 The President and Fellows of Harvard College and the Massachusetts Institute of Technology.