User’s Guide : Basic Single Equation Analysis : Instrumental Variables and GMM : Background
A fundamental assumption of regression analysis is that the right-hand side variables are uncorrelated with the disturbance term. If this assumption is violated, both OLS and weighted LS are biased and inconsistent.
There are a number of situations where some of the right-hand side variables are correlated with disturbances. Some classic examples occur when:
There are endogenously determined variables on the right-hand side of the equation.
Right-hand side variables are measured with error.
For simplicity, we will refer to variables that are correlated with the residuals as endogenous, and variables that are not correlated with the residuals as exogenous or predetermined.
The standard approach in cases where right-hand side variables are correlated with the residuals is to estimate the equation using instrumental variables regression. The idea behind instrumental variables is to find a set of variables, termed instruments, that are both (1) correlated with the explanatory variables in the equation, and (2) uncorrelated with the disturbances. These instruments are used to eliminate the correlation between right-hand side variables and the disturbances.
There are many different approaches to using instruments to eliminate the effect of variable and residual correlation. EViews offers three basic types of instrumental variable estimators: Two-stage Least Squares (TSLS), Limited Information Maximum Likelihood and K-Class Estimation (LIML), and Generalized Method of Moments (GMM).