Estimation of an implicit regression model. Numerical solutions with the NAG library. Observations from an example

For an econometric problem, we arrived at an implicit regression model. The estimation was realised with the NAG library. Here we intend to give an account of our experience with NAG, with respect to the routines we used. We also try to bring out some practical principals the statistician would follow when faced with the estimation of a nonstandard regression model. Most of our observations are drawn from the implementation of the Instrumental Variables Method.