Simultaneity, Instrumental Variables and Non-Normal Errors

Abstract

Simultaneity occurs when the regressor and the error are no longer independent, as is required in the classical assumptions. This leads to simultaneity bias, while other violations of this assumption, which can occur regularly with economic data, also lead to biased estimates, in particular when autocorrelation and a lagged dependent variable appear together. Instrumental variables estimation is a potential solution to this problem. The presence of non-normally distributed errors may be symptomatic of important misspecifications that could easily lead to very misleading and, in some cases, completely ridiculous coefficient estimates. Residuals should be examined for the presence of outliers and a test for non-normality is presented, with examples being used to illustrate the impact and mitigation of outlying observations.