We propose to model endogeneity bias using prior distributions of moment conditions. The estimator can be obtained both as a method-of-moments estimator and in a Ridge penalized regression framework. We show the estimator’s relation to a Bayesian estimator.

An additivity property of LM tests is derived, linking joint, marginal and Bera-Yoon "adjusted" tests, hence the latter can be derived as the difference of the first two. An artificial regression framework provides an intuitive geometrical illustration of the Bera-Yoon principle.