When independent variables are measured with error, ordinary least squares regression can yield parameter estimates that are biased and inconsistent.

This article documents an inflation of Type I error rate that can also occur.  In addition to analytic results, a large-scale Monte Carlo study shows unacceptably high Type I error rates under circumstances that could easily be encountered in practice. A set of smaller-scale simulations indicate that the problem applies to various types of regression and various types of measurement error.