Endogenous Variable
An endogenous variable is a variable whose value is determined within a model, as a function of the other variables in the system, rather than being imposed from outside. It stands in contrast to an exogenous variable, whose value is taken as given and is not explained by the model. The distinction is fundamental to economic modelling, since the choice of which variables are endogenous and which are exogenous defines the structure of a model and determines what the model can explain and what it must assume.
The distinction
In a simple supply and demand model, price and quantity are endogenous, because they are determined by the interaction of demand and supply. The determinants of demand, such as income and tastes, and the determinants of supply, such as input prices and technology, are usually treated as exogenous, because they are taken as given when the model is solved. Solving the model means finding the values of the endogenous variables that satisfy all the relationships simultaneously.
The classification is not inherent in the variables themselves but depends on the model and on the purpose of the analysis. Income may be exogenous in a partial equilibrium model of a single market, but it becomes endogenous in a general equilibrium model in which income is determined by production and trade. Similarly, the exchange rate may be exogenous in a model of a small open economy with a fixed rate, or endogenous under a floating rate. The same variable can be treated differently in different models.
Simultaneity and identification
Endogeneity creates a statistical problem. When an explanatory variable is determined within the system, it may be correlated with the error term, violating a key assumption required for ordinary least squares estimates to be unbiased and consistent. For example, in estimating a demand curve, price and quantity are determined jointly, so regressing quantity on price does not recover the demand curve unless the supply curve is identified. This problem, known as simultaneity, is central to econometrics.
To address it, economists use simultaneous equation methods, such as instrumental variables, two-stage least squares, and full-information methods. These techniques require instruments, variables that are correlated with the endogenous regressor but uncorrelated with the error term, and the validity of the instruments is essential to the credibility of the estimates. The search for credible identification strategies, including natural experiments and randomised trials, has shaped modern empirical economics.
Dynamics and expectations
In dynamic models, the distinction between endogenous and exogenous variables interacts with time and expectations. A variable that is exogenous in the current period may be endogenous in the next, and expectations about future values can influence current decisions. In rational expectations models, expectations are themselves endogenous, formed from the same information and structure that determine outcomes, so that the model's predictions depend on how agents form beliefs.
This interdependence has important implications. A policy change may alter the behaviour of agents if it changes the rules or the information they use to form expectations, so that the effects of policy cannot be inferred from historical relationships alone, a point emphasised in the critique associated with Robert Lucas. Endogenous expectations therefore complicate forecasting and policy evaluation and motivate models in which behaviour is derived from underlying preferences and constraints.
Uses in modelling
The classification of variables guides the construction and solution of economic models. In macroeconomics, models differ in whether consumption, investment, prices, and interest rates are treated as endogenous, and these choices determine whether the model can address questions about the effects of policy. In growth theory, output, capital, and technology may be endogenous, and the modelling of endogenous technical change has been a major research programme.
The distinction also matters for interpretation. When a model predicts that a change in an exogenous variable will alter an endogenous one, the prediction is conditional on the model's structure and on the assumption that the exogenous variable is truly independent of the system. Careful specification, testing, and sensitivity analysis are needed to ensure that the classification is defensible and that the conclusions are robust.
Endogeneity in practice
In applied work, endogeneity arises in many forms. Omitted variables, which are unobserved determinants of both the dependent variable and an explanatory variable, create correlation between the regressor and the error term. Measurement error in an explanatory variable causes attenuation and inconsistency. Reverse causality, in which the dependent variable influences the explanatory variable, produces simultaneity. Each of these problems must be addressed for estimates to be interpreted causally.
Researchers use a range of strategies to address endogeneity. Instrumental variables use an external source of variation in the endogenous regressor. Panel methods, such as fixed effects, control for unobserved heterogeneity that is constant over time. Difference-in-differences exploits policy changes that affect some units but not others. Regression discontinuity exploits thresholds that determine treatment. Each strategy has assumptions that must be defended, and the credibility of the resulting estimates rests on those assumptions.
Policy evaluation and structural models
The classification of variables is central to policy evaluation. To estimate the effect of a policy change, the analyst must identify variation in the policy that is not caused by the outcome of interest. Randomised controlled trials provide the cleanest source of such variation and have become common in development economics and in the evaluation of social programmes. Natural experiments, including changes in laws and eligibility rules, offer alternatives where randomisation is impossible.
Structural models take a different approach. Rather than relying on reduced-form variation, they specify the preferences and constraints of agents and estimate the parameters of the model, using the full set of relationships to simulate the effects of policy. Structural models can answer questions about policies that have never been tried, but their conclusions depend on the assumed structure, and the assumptions must be tested and justified. The choice between reduced-form and structural approaches depends on the question and on the available data.
Implications for forecasting
The distinction between endogenous and exogenous variables also matters for forecasting. Forecasts of endogenous variables are conditional on assumptions about the paths of exogenous variables, and errors in those assumptions translate into errors in the forecast. In macroeconomic forecasting, assumptions about oil prices, global growth, and policy are typically exogenous inputs, and the forecast of domestic output, inflation, and employment follows from the model.
When relationships change, as they do when policies shift or when structural change occurs, historical relationships may no longer hold, and the model's predictions may be unreliable. This problem, associated with the critique of policy evaluation under changing rules, motivates the use of models in which behaviour is derived from primitives and in which expectations are modelled explicitly. The careful specification of which variables are endogenous and which are exogenous is therefore not a technical detail but a substantive choice with consequences for the conclusions.