If you study enough econometrics, you will eventually come across an asymptotic argument in which some parameter is assumed to change with sample size. This peculiar notion goes by a variety of names including “Pitman drift,” a “sequence of local alternatives,” and “local mis-specification,” and crops up in a wide range of problems from weak instruments, to model selection, to power analysis.

In this post we’ll examine a very simple instrumental variables model from three different perspectives: two familiar and one a bit more exotic. While all three yield the same solution in this particular model, they lead in different directions in more complicated examples.