# Instrumental Variable

Instrumental variable is a very important technique that is applied in statistics and econometrics. However, it can be a bit confusing to most people. The technique is used in the estimation of casual relationships when controlled experiments are not feasible or when a treatment is not is not delivered successfully to each unit in an experiment that is not randomized. There are various instrumental variable methods that can be applied in obtaining results. These methods allow for consistency in estimation under conditions that explanatory variables are correlated with the error terms of a relationship of regression.

## How instrumental variable operates

The estimation of causal impacts is often faced with difficulties. In fact, even trials that are randomized are imperfect, partly because we can often not be able to carry out true experiments. However, it is important to note that experimental design still remains the gold standard of statistical research. Instrumental variable is among the quasi-experimental methods of impacts estimations that are too compelling. The reason for this is because the assumptions required for the justification of instrumental variable method are usually more plausible than those that are required to justify other methods like regression.

In order to estimate an instrumental variable model, one should begin by identifying a variable or certain variables that impact the key independent variable, but only affect the results through the main independent variables. For instance, you can assume that month and state of birth would have no impact of a person’s income later in life, except that state laws establish when one is able to begin and end his or her K-12 education.

It is important to note that the models of instrumental variable are often conceptualized as two different equations. One of them specifies the relationship that exists between the main independent variable and the result. The other equation specifies the relationship between the instrumental variables and the result. Despite linear regression being considered to generally produce biased and inconsistent estimates, accurate results (consistent estimates) can still be obtained if an instrument is available. An instrument refers to a variable that does not itself belong in the explanatory equation, and has got a correlation with the endogenous variables.

There are two main requirements for using instrumental variable in linear regression. One is that the instrument must be correlated with the endogenous explanatory variables, limited to other covariates. Besides, the instrument cannot be correlated with the error term in the explanatory equation; the instrument cannot be left to face the same problem as the original predicting variable.

Instrumental variable methods are mostly used in the estimation of causal effects in contexts whereby controlled experiments are not available. However, the credibility of the resulting estimates is based on the choice of suitable instruments to use. Good instruments are often developed from policy changes. For instance, when a federal student aid scholarship program is cancelled, it may give a revelation of the effects of aid on the outcomes of some students.

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### Reference:

http://www.urban.org/toolkit/data-methods/instrumental.cfm

http://en.wikipedia.org/wiki/Instrumental_variable