Language
Country/Area
No result found
Why not use randomized experiments? Uncover the secrets behind instrumental variables!
In statistics, econometrics, epidemiology, and related disciplines, instrumental variables (IV) methods are used when controlled experiments are not feasible or when the desired treatment is not successfully delivered to every unit. The core of this approach is the estimation of causal relationships, which enables researchers to seek valid causal inferences even in the absence of randomized experiments.
Instrumental variables are used to solve the endogeneity problem between the explanatory variables and the error term.
Endogeneity is a common problem. In a regression model, if the explanatory variables are correlated with the error term, the results of ordinary least squares (OLS) and analysis of variance (ANOVA) will be biased and inconsistent. The effectiveness of instrumental variables lies in their ability to reveal the causal effect of an explanatory variable (such as smoking) on a dependent variable (such as health status).
For example, when a researcher wants to estimate the effect of smoking on health, he or she will find that a correlation between smoking and health does not mean that smoking directly causes poor health, because there may be other variables, such as depression, that affect both. . Furthermore, instrumental variables become key when it is not possible to conduct controlled experiments on the entire population.
If researchers can find a variable that is correlated with smoking but does not directly affect health, such as cigarette tax rates, then they can use that variable to make causal inferences.
Cigarette tax rate was chosen as an instrumental variable precisely because it can be reasonably inferred that it affects health only by affecting smoking. If the results of the study showed a correlation between cigarette tax rates and health status, this would be considered evidence of the negative health effects of smoking.
Historical Background of Instrumental Variables
The concept of instrumental variables originated from the work of Philip G. Wright in 1928, who analyzed the production, transportation, and sales of vegetable and animal oils in the early United States. In 1945, Olav Reiersøl applied this method in his paper and gave it the name "instrumental variable". Wright used this approach when investigating the supply and demand of butter because he realized that price affects both supply and demand, making it impossible to construct either a demand or supply curve based on observational data alone.
Wright cleverly chose rainfall as his instrumental variable because rainfall affects forage production, which in turn affects milk production, but does not affect the demand for butter.
Over time, instrumental variable theory has been further developed in many studies, especially in applications in econometrics, providing useful analytical tools. Judea Pearl's formal definition of instrumental variables in 2000 paved the way for subsequent research, while Angrist and Krueger's research briefly outlined the history and application background of these techniques.
Theoretical basis
The theoretical basis for instrumental variables extends to a wide range of models, but is particularly common in applications to linear regression. Traditionally, instrumental variables must satisfy two key conditions: they must be correlated with the endogenous explanatory variable but not with the error term. If these conditions are met, instrumental variables can provide support for estimation and address the challenges faced by the OLS method in terms of endogeneity.
The effectiveness of an instrumental variable depends on its correlation with the endogenous variable and its independence from the error term.
Understanding the role of instrumental variables also requires graphical representation. By using causal diagrams, researchers can quickly determine whether a variable qualifies as an instrumental variable. For example, if researchers wish to estimate the impact of a college tutoring program on academic achievement, they are likely to encounter confounding problems caused by multiple factors. This is the case when random assignment of dormitories makes proximity to a tutoring program a reasonable instrumental variable.
Ultimately, instrumental variables methods provide an efficient and valuable way to explore the world of causal inference. It helps researchers overcome the limitations of randomized experiments and provides new ideas for analyzing many causal problems. In this process, we cannot help but ask: In the face of increasingly complex social problems, can instrumental variables truly solve all the causal inference problems we face?
