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What if you can't control the experiment? Why instrumental variables are the key to solving bias!
In statistics, econometrics, epidemiology and other related disciplines, instrumental variables (IV) methods are widely used to estimate causal relationships when controlled experiments are not feasible or treatments cannot be successfully delivered to every unit. relation. Simply put, when you encounter the problem of correlation between the explanatory variables and the error term, using instrumental variables can avoid biased results.
The intuitive understanding of using instrumental variables is that when the researcher's independent variable X (explanatory variable) is affected by the error term U, the conventional least squares method (OLS) may lead to biased estimates, while the IV method A consistent estimate can be obtained.
For example, suppose a researcher wants to analyze the causal effect of smoking (X) on general health status (Y). The correlation between smoking and health based solely on observational data does not mean that smoking causes poor health, because there are other variables such as depression that may affect both smoking and health. In this case, researchers cannot conduct a randomized controlled trial.
Researchers could consider using tobacco tax rates (Z) as an instrumental variable for smoking, provided that the tax rate is only associated with health in a way that is mediated by smoking. If a study finds a link between tobacco tax rates and health conditions, it would be seen as evidence that smoking may affect health.
The history of instrumental variables can be traced back to 1928, when Philip G. Wright first proposed the concept. Wright's research focuses on the supply and demand of butter in the United States, and he believes that climate factors can serve as a suitable instrumental variable to describe this process. This idea led to the gradual formation and development of the instrumental variable method in econometrics.
So, how to choose appropriate instrumental variables? For an instrumental variable to be effective, two main conditions must be met: first, the instrumental variable must be correlated with the endogenous explanatory variable; second, the instrumental variable must be uncorrelated with the error term. These two conditions are essential to obtain consistent estimates.
In addition, the selection of appropriate instrumental variables should also consider their effectiveness in the specific research context. At this time, researchers can use causal diagrams to visualize the relationship between variables. In some cases, a variable may become an effective instrumental variable after controlling for other variables.
For example, if we want to estimate the effect of a college counseling program on students' GPA, if the distance students travel to the counseling program is taken into account, this may be an instrumental variable that assigns a causal effect to the program, but Assess the possible impact of distance on students’ low achievement.
Today, many relevant literatures have fully explored the application of instrumental variables and their practical cases in different fields. For example, Angrist and Krueger demonstrated the application of instrumental variable methods in educational economics in 2001 to analyze the causal relationship between academic qualifications and income.
This suggests that when traditional regression analysis cannot provide precise causal estimates due to confounding factors, the instrumental variable approach can make up for this shortcoming. However, the selection of appropriate instrumental variables relies on a good theoretical foundation and a deep understanding of the data generating process.
In summary, instrumental variables, as a key method to resolve bias, provide researchers with an effective analytical tool when it is impossible to conduct a controlled experiment. However, in your research, can you accurately select effective instrumental variables and reveal the implicit causal relationship?
