AndersonRubinSchätzung

AndersonRubinSchätzung is a statistical concept that refers to the Anderson–Rubin test used in the context of linear models with instrumental variables. The test is particularly relevant when applied to simultaneous-equation models or in estimating parameters where endogeneity problems arise. It provides a method of testing the joint null hypothesis that a set of endogenous explanatory variables are irrelevant, while allowing for heteroskedasticity in the error terms. Importantly, the Anderson–Rubin test remains valid even when the standard assumption of exogenous instruments fails, as long as the test is used to assess the relevance of the instruments themselves.

The test statistic is derived from the joint significance of the instruments in a reduced‑form regression. In practice, the procedure involves estimating a first‑stage regression of the endogenous variables on all instruments, computing the residuals, and then forming a chi‑square statistic whose degrees of freedom equal the number of instruments excluded. A large value of the statistic leads to rejection of the null, indicating that at least one of the instruments contributes significantly to explaining the variation in the endogenous regressors.

One key advantage of the Anderson–Rubin approach is its robustness to weak‑instrument scenarios. Compared with alternative tests such as the Hausman or the Durbin–Wu–Hausman tests, the Anderson–Rubin statistic does not rely on the consistency of the first‑stage estimates under the null hypothesis. Consequently, it is especially useful in applications where the strength of the instruments is uncertain.

In econometrics and related fields, the Anderson–Rubin test is widely taught as part of the toolbox for instrumental‑variable analysis. It is commonly implemented in statistical software packages through built‑in commands that automatically compute the statistic and its associated p‑value, making it accessible to practitioners working with complex endogenous systems.