earnings and income. The results here show that in S ∗ well-posedness holds more generally: as long as the error distribution is not super-smooth. The solutions for the systems of convolution equations can be used in plug-in estimation. Properties of nonparametric plug-in estimators are based on results on stochastic convergence in S ∗ for the solutions that are stochastic functions expressed via the estimators of the known functions of the observ- ables. Section 2 of the paper enumerates the classes of models considered here. They are divided into three groups: 1. measurement error models with classi- cal and Berkson errors and possibly an additional measurement, and common factor models that transform into those models; 2. nonparametric regression models with classical measurement and Berkson errors in variables; 3. mea- surement error and regression models with conditional independence. The corresponding convolution equations and systems of equations are provided and discussed. Section 3 is devoted to describing the solutions to the convolu- tion equations of the models. The main mathematical aspect of the different models is that they require solving equations of a similar form. Section 4 pro- vides a table of identified solutions and discusses partial identification and well-posedness. Section 5 examines plug-in estimation. A brief conclusion follows. 7