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 functions of the exogenous variables, if any. In econometrics, the equations of a structural form model are estimated in their theoretically given form, while an alternative approach to estimation is to first solve the theoretical equations for the endogenous variables to obtain reduced form equations, and then to estimate the reduced form equations.

Let Y be the vector of the variables to be explained (endogeneous variables) by a statistical model and X be the vector of explanatory (exogeneous) variables. In addition let ${\displaystyle \varepsilon }$ be a vector of error terms. Then the general expression of a structural form is ${\displaystyle f(Y,X,\varepsilon )=0}$, 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 ${\displaystyle Y=g(X,\varepsilon )}$, with g a function.