The asymptotic and finite sample (un)conditional distributions of OLS and simple IV in simultaneous equations

In practice structural equations are often estimated by least-squares, thus ne-
glecting any simultaneity. This paper reveals why this may often be justifiable
and when. Assuming data stationarity and existence of the first four moments of
the disturbances we study the limiting distribution of the ordinary least-squares
(OLS) estimator in a linear simultaneous equations model. In simple static mod-
els we compare the asymptotic e¢ ciency of this inconsistent estimator with that
of consistent simple instrumental variable (IV) estimators and depict cases where
- due to relative weakness of the instruments or mildness of the simultaneity -
the inconsistent estimator is more precise. In addition, we examine by simulation
to what extent these first-order asymptotic findings are reflected in finite sam-
ples, taking into account non-existence of moments of the IV estimator. In all
comparisons we distinguish between conditional and unconditional (asymptotic)
distributions. By dynamic visualization techniques we enable to appreciate any
di¤erences in e¢ ciency over a parameter space of a much higher dimension than
just two, viz. in colored animated image sequences (which are not very e¤ective
in print, but much more so in live-on-screen projection).