On the nature and discovery of structure.

*(English)*Zbl 0579.62095Summary: Extending principles of experimentation, we discuss conditions under which nonexperimental data allow consistent estimation of effects of the kind revealed by experimentation and relevant to decisions. We show how implications of these conditions are often overlooked and how failure to distinguish between ”factors” and ”concomitants” makes almost anything said about a model ambiguous if not wrong.

The effects to be estimated dictate the factors to be included; consistency and efficiency determine the concomitants, whose effects are not to be estimated. Concomitants may affect but must not be affected by the factors. Effects of excluded variables on an included variable may cause inconsistency if the included variable is a factor, can only reduce inconsistency if the included variable is a concomitant. Exclusion of a variable because it is highly correlated with another may sometimes be legitimate if both variables are concomitants, never if either is a factor.

A condition for consistent estimation stated in virtually every book on econometrics is meaningless in one common form, impossible to satisfy in another. The distinction between exogenous and other predetermined variables is irrelevant to consistent estimation of the effects of predetermined variables. The relation of predetermined to excluded variables is irrelevant to consistent estimation of the effects of endogenous variables.

The effects to be estimated dictate the factors to be included; consistency and efficiency determine the concomitants, whose effects are not to be estimated. Concomitants may affect but must not be affected by the factors. Effects of excluded variables on an included variable may cause inconsistency if the included variable is a factor, can only reduce inconsistency if the included variable is a concomitant. Exclusion of a variable because it is highly correlated with another may sometimes be legitimate if both variables are concomitants, never if either is a factor.

A condition for consistent estimation stated in virtually every book on econometrics is meaningless in one common form, impossible to satisfy in another. The distinction between exogenous and other predetermined variables is irrelevant to consistent estimation of the effects of predetermined variables. The relation of predetermined to excluded variables is irrelevant to consistent estimation of the effects of endogenous variables.

##### MSC:

62P20 | Applications of statistics to economics |

62A01 | Foundations and philosophical topics in statistics |

62J99 | Linear inference, regression |