Reduced Form

Reduced Form

In statistics, and particularly in econometrics, the reduced form of a system of equations is the result of solving the system for the endogenous variables. This gives the latter as a function of the exogenous variables, if any. In econometrics, "structural form" models begin from deductive theories of the economy, while "reduced form" models begin by identifying particular relationships between variables.

Let Y and X be random vectors. Y is the vector of the variables to be explained (endogeneous variables) by a statistical model and X is the vector of explanatory (exogeneous) variables. In addition let be a vector of error terms. Then the general expression of a structural form is, where f is a function, possibly from vectors to vectors in the case of a multiple-equation model. The reduced form of this model is given by, with g a function.