Instrumental Variables for Logistic Regression: An Illustration

The estimated effect of a regressor on an outcome is inconsistent when that regressor is determined simultaneously with that outcome. Instrumental variables estimation is a means of obtaining consistent parameter estimates in this situation. The best-known form of instrumental variables is two-stage least squares; unfortunately, this procedure cannot be simply extended to non-linear models such as logistic regression. Instrumental variables estimation, however, is still possible, and using the Generalized Method of Moments, this paper is the first to produce instrumental variables estimates for logistic regression. Obtaining these estimates is easy using widely available software. An illustrative example is provided. This methodology should be useful to social scientists familiar with 2SLS and logistic regression.