Instrumenttilähestymiset

Instrumenttilähestymiset, often translated as instrumental approaches, is a concept used in various fields, particularly in economics and social sciences, to address issues of endogeneity and omitted variable bias in statistical analysis. When a direct causal relationship between an independent variable (X) and a dependent variable (Y) is difficult to establish due to unobserved factors that influence both X and Y, or when X is itself determined by other variables that also affect Y, researchers may turn to instrumental variables.

An instrumental variable (Z) is a variable that is correlated with the endogenous independent variable (X) but is not directly correlated with the dependent variable (Y), except through its effect on X. Furthermore, the instrument Z must not be correlated with any omitted variables that affect Y. The core idea is to use the variation in X that is explained by Z to estimate the causal effect of X on Y. This isolates a source of variation in X that is arguably exogenous.

The most common method for estimating models with instrumental variables is Two-Stage Least Squares (2SLS). In the first stage, the endogenous variable X is regressed on the instrumental variable(s) Z and any exogenous covariates. The predicted values of X from this regression are then used in the second stage as a proxy for X, and these predicted values are regressed on Y along with the exogenous covariates. This process effectively purges X of the part that is correlated with the error term, providing a less biased estimate of the causal effect of X on Y.

The validity of instrumental variable estimation hinges critically on the assumptions about the instrument. These include relevance (the instrument must be correlated with the endogenous variable) and exogeneity (the instrument must be uncorrelated with the error term). Violations of these assumptions can lead to biased or inconsistent estimates. The development of instrumental variable methods has been a significant contribution to econometrics, enabling more robust causal inference in observational studies.