Instrumental Variable
Instrumental variable is used in estimating casual relationships when a treatment is not delivered to all units successfully or a controlled experiment is not feasible in a randomized experiment in statistics, epidemiology, econometrics and other related disciplines.
Philip G. Wright derived the instrumental variable theory for the first time in a book entitled; The Tariff on Animal and Vegetable Oils. Instrumental variables are traditionally defined as variable Z with a correlation with an independent variable X without a correlation with the error term U in an equation.
The equation is as follows:
Y= βX +U
However, this definition has concept ambiguities that include independent variable and error term. This has caused confusion regarding the meaning that this equation has and it has been labeled as “regression” wrongly.
The method of instrumental variable allows for consistent estimation in the experiments with correlated explanatory
variables with error terms of regression relationships. This correlation can occur when one of the explanatory variables is caused by a dependent variable, when the explanatory variables are subjected to measurement errors or when relevant covariates or explanatory variables are omitted in the model.
In any of these situations, inconsistent and biased estimates are generally produced by linear regression. Nevertheless, if there is an instrument variable, it is still possible to obtain consistent estimates. An instrument variable refers to a variable that is not part of the explanatory equation. It is correlated to endogenous covariates that are condition to the other explanatory variables.
In a linear model, using instrumental variable has two major requirements. First, the instrument has to be correlated to the endogenous covariates that are conditional to other explanatory variables. Second, the instrument should not be correlated to the error term in covariates equation. This implies that the instrument should not suffer from a similar problem with an original, predicting variable.
The method of instrumental variable has been used in estimating policy variable of the effects of a treatment in an experimental design that is not feasible and it has been successful. Estimating the casual impacts has several difficulties. Even randomized experiments are not perfect in some parts because researchers can seldom, if possible, perform true experiments.
Instrumental variable analysis is one of the most compelling quasi-experimental methods that are used in estimating impacts since the assumptions required to provide justification for the instrumental method are more plausible that the ones required in justifying other experimental methods.
Researchers have proposed the instrumental variable method as one of the potential approaches in solving common problems of the uncontrolled confounding in the comparative studies in medical interventions. Over the years, several reviews have been done on the instrumental variable methods in biomedical and statistical literature at different technical levels and substantive emphases have been made. However, many researchers are still unfamiliar with instrumental variable and its application.
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Instrumental variable method has been used in estimating casual relationships in epidemiology, econometrics and statistics among other disciplines. However, you must conduct an extensive study to write a quality essay about this method. Nevertheless, you can order this essay with veteran writers at Essays Experts.
Sources
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2886161/
http://en.wikipedia.org/wiki/Instrumental_variable
http://www.urban.org/toolkit/data-methods/instrumental.cfm