Instrumental Variables

INSTRUMENTAL VARIABLES

Instrumental variables

An instrumental variable is termed as a variable Z that correlates with the independent variable X and is uncorrelated with the error term U in the equation

[pic] (Petrakēs, 2014).

There are many methods that can be used to estimate causal effects in the contexts that the controlled experiments are not available. Best instruments are usually created by changes in policy. For instance, the cancelation of a federal student-aid scholarship program may show the effects of aid on the outcomes of some students. Some natural and quasi-natural experiments of various types may also be used such as the use of weather shocks to identify the effects of economic growth changes. Instrumental variables methods are usually used to solve various problems that are encountered in the OLS regression. The problems may include; omitted variable bias, measurement error and simultaneity or reverse causality (Petrakēs, 2014).

Instrumental variables are used to estimate causal relationships especially when experiments that are controlled are not seen or when a treatment is not delivered successfully to every unit in an experiment that is randomized. They also allow consistent estimation when the explanatory variables are correlated with the error terms of a regression relationship. Such a correlation can occur when the dependent variables cause at least one of the covariates, when there are relevant explanatory variables that are omitted from the model. It can also happen when the covariates are subject to the measurement error. In such a situation, ordinary linear regression usually produces inconsistent and based estimates. On the other hand, if an instrument is available, the consistent estimates may still be obtained. An instrument is usually a variable that does not belong itself in the explanatory equation, and it is correlated with the endogenous explanatory variables, conditional on the other covariates. In the linear...