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Did you know how instrumental variables help reveal true causal relationships?
In related disciplines such as statistics, econometrics, and epidemiology, instrumental variable (IV) methods can be used when controlled experiments cannot be performed or when the treatment is not successfully delivered to every sample in a randomized experiment. to estimate causality. The main purpose of instrumental variables is to help discover causal relationships that may exist when independent variables are related to error terms, especially in the case of bias when using the traditional least squares method (OLS).
The effectiveness of instrumental variables lies in the fact that they can induce changes in the independent variables, but they have no independent effect on the dependent variable and are not related to the error term, so that researchers can reveal the causal impact between the independent variables and the dependent variable. .
Instrumental variables methods allow researchers to make consistent estimates when explanatory variables (covariates) are related to the error terms in a regression model. This correlation may occur in the following situations: "reverse" causality between variables, omitted variables affecting the independent and dependent variables, or variable problems caused by measurement error. In this case, the OLS algorithm produces biased and inconsistent estimation results. However, if valid instrumental variables can be found, consistent estimates can be obtained despite the problems.
Instrumental variables are generally defined as variables that are not in the independent variable equation but are relevant to the endogenous independent variables. Using the stage test, if the instrumental variable has a strong correlation with the endogenous independent variable, the instrumental variable is called a strong first stage, otherwise it may lead to misleading parameter estimates and standard errors.
In the sampled data, an association between smoking (X) and health (Y) is observed, but this does not mean that smoking causes ill health, as other variables such as depression may affect both.
Specifically, researchers may not be able to conduct controlled experiments in the general population to directly assess the health effects of smoking, so they may use the tax rate on tobacco products (Z) as an instrumental variable for smoking. Assuming that these tax rates affect health only through smoking, researchers can estimate the benign health effects of smoking from observational data.
The history of instrumental variables can be traced back to 1928, first proposed by Philip G. Wright, who used grain and animal oil production and sales data to explore the relationship between demand and supply. Olav Reiersøl applied this idea in his paper in 1945 and named the method. For example, Wright chose to use regional rainfall as the instrumental variable required for his analysis because he confirmed that rainfall affects the supply of dairy products but not demand.
If the definition of instrumental variables can separate the uncorrelated and error terms, it can further reveal the causal relationship.
This kind of causality is very important in economics, especially in econometric models. In fact, these two conditions are the basic requirements for the use of IV when we try to use a linear regression model in which the instrumental variable Z is related to the independent variable X but not related to the error U. The error U should be composed of all exogenous factors and should not affect the dependent variable Y when controlling for X. This means that researchers need to have background knowledge about the data generation process in order to select appropriate instrumental variables.
As an example, suppose we want to estimate the impact of a college tutoring program on students' grade point average. Students participating in the program may have their GPAs affected by factors such as grade concerns or academic difficulties. If students are randomly assigned to dormitories, the distance between their dormitory and cram school may become an effective instrumental variable. If the cram school is set up in a school library, the correlation between distance and GPA may show interference from other factors, so other covariates need to be added to maintain its validity.
Ultimately, choosing appropriate instrumental variables is key, as inappropriate instrumental variables may lead to erroneous conclusions. At the same time, using graphical representation can help researchers quickly determine whether variables meet the IV criteria. Revealing these causal relationships can not only help researchers obtain consistent estimates, but also provide clearer policy recommendations and implementation paths.
In today’s complex data environment, are there other ways to effectively reveal potential causal relationships?
