When measurement errors are present, the linear model and probit model are unidentifiable if the covariate is normally distributed. Thus, one usually requires extra information or assumptions to proceed the analysis. However, we think that the unidentifiability are special cases and will not happen for other distributions of the covariate. When there is no extra information, we propose an overparameterization method to estimate the regression parameters and the variance of the measurement error. We provide a theoretical verification and a conjecture for when the model can be analyzed consistently by the proposed method. A simulation study was conducted and seems to be coincided with the theoretical results.