# Exogeneity and endogeneity

In statistics and econometrics , it is important to differentiate between exogeneity and endogeneity , since disregarding this can lead to distorted results. In the presence of an exogenous explanatory variable , one speaks of exogeneity and in the presence of an endogenous explanatory variable of endogeneity.

## Endogeneity

Bias of the KQ estimator caused by endogeneity

In regression analysis , endogeneity (from " endogenous ") means that there is a connection between the explanatory (independent) variables and the disturbance variable . An endogenous explanatory variable correlates with the confounding variable. This means that the covariance of the explanatory variables and the disturbance variable is not equal to zero:

${\ displaystyle \ operatorname {Cov} (x_ {ik}, u_ {i}) \ neq 0}$

It is important that there is as little endogeneity as possible, otherwise the estimates will be inconsistent and the estimate will be biased. To test endogeneity, there are endogeneity tests such as the Hausman specification test .

### causes

• Distortion by exuberant variables (engl. Omitted variable bias ): distortion that which is correlated with the explanatory variable considered a relevant explanatory variables is induced by not taking into account at least. If it is because relevant variables have been neglected, one speaks of underfitting , and if there are too many explanatory variables of overfitting .
• Simultaneous causality , that is, when more than one equation is required to describe a relationship, and this leads to feedback mechanisms.
• Measurement error in the explanatory variable.
• Autocorrelation with delayed endogenous variables.

### Solution strategies

One possible remedy is to use an estimator in the fixed effects model in conjunction with panel data . Other commonly used techniques are instrument variable estimation and regression discontinuity analysis .

## Exogeneity

In the context of time series analysis , exogeneity means that one variable is not fed back to the other. Causality is closely related to the concept of exogeneity . In connection with stochastic models there are three concepts of exogeneity.

### Strict exogeneity

The strict exogeneity means that the observations of a variable x at any point in time t are independent of the realizations of the disturbance vector. For non-linear models or models with rational expectations , strict exogeneity has to be defined differently. The strict exogeneity facilitates and simplifies the statistical inference of the models.

### Weak exogeneity

Weak exogeneity means that the inference for a certain amount of model parameters can be conditioned on the present realizations of these variables without loss of information. To use an estimation method for the parameters of a model, it is sufficient if there is weak exogeneity. In the DSE model, weak exogeneity follows from strict exogeneity if all parameters in the distribution of -s are superfluous parameters. In contrast to the strict exogeneity, which can be tested on its own (e.g. Hausman specification test ), the weak exogeneity, which is linked to certain parameters, can only be tested in conjunction with other hypotheses . ${\ displaystyle x_ {t}}$

### Super exogenicity

The super exogeneity has to be seen in connection with the Lucas criticism . This means that economic subjects adapt their behavior (e.g. measured by the values ​​of regression parameters ) to the economic environment . The parameters are conditioned to an environment described by the characteristics of certain variables. If the events on which the economic agents orient their behavior are exogenously determined variables (policy variables), then this dependency of the parameters must be modeled explicitly . Superexogeneity now means that the Lucas critique does not apply to a variable.

## Individual evidence

1. Herbert Stocker: Methods of Empirical Economic Research http://www.uibk.ac.at/econometrics/einf/kap11.pdf