What is Reduced Form?

The Concept of Reduced Form in Econometrics Defined

Math equations
Math equations. Getty Images/BlandineSchillinger/Moment

In econometrics, the reduced form of a system of equations is the product of solving that system for its endogenous variables. In other words, the reduced form of an econometric model is one that has been rearranged algebraically so that each endogenous variable is on the left side of one equation and only predetermined variables (like exogenous variables and lagged endogenous variables) are on the right side.

Endogenous Variables versus Exogenous Variables

To fully understand the definition of reduced form, we must first discuss the difference between endogenous variables and exogenous variables in econometric models. These econometric models are often complicated. One of the ways researchers break these models down is by identifying all of the various pieces or variables. In any model, there will be variables that are created or impacted by the model and others that remain unchanged by the model. Those that are changed by the model are considered endogenous or dependent variables, whereas those that remained unchanged are the exogenous variables. Exogenous variables are assumed to be determined by factors outside of the model and are therefore the autonomous or independent variables.

Structural Form versus Reduced Form

Systems of structural econometric models can be constructed purely based upon economic theory, which can be developed through some combination of observed economic behaviors, knowledge of policy that influences economic behavior, or technical knowledge.

Structural forms or equations are based on some underlying economic model.

The reduced form of a set of structural equations, on the other hand, is the form produced by solving for each dependent variable such that the resulting equations express the endogenous variables as functions of the exogenous variables.

 Reduced form equations are produced in terms of economic variables that may not have their own structural interpretation. In fact, a reduced form model does not require additional justification beyond the belief that it could work empirically.

Another way to look at the relationship between structural forms and reduced forms is that structural equations or models are generally considered deductive or characterized by "top-down" logic whereas reduced forms are generally employed as a piece of some larger inductive reasoning.

Structural Models versus Reduced Form Debate

The debate surrounding the use of structural forms versus reduced forms is a hot topic among many economists. Some even see the two as opposing modeling approaches. But in reality, structural form models are simply restricted reduced form models based upon different information assumptions. In short, structural models assume detailed knowledge whereas reduced models assume less detailed or incomplete knowledge of the factors. Many economist now agree that the modeling approach that is preferred in a given situation is dependent on the purpose for which the model is being used. For instance, many of the core pursuits in financial economics are more descriptive or predictive exercises, which can be effectively modeled in reduced form since the researchers do not necessarily require some deep structural understanding (and often do not have that detailed understanding).