The asymptotic and finite sample distributions of OLS and simple IV in simultaneous equations

In practice structural equations are often estimated by least-squares, thus neglecting any simultaneity. This paper reveals why this may often be justi…able and when. Assuming data stationarity and existence of the …rst four moments of the disturbances we …nd the limiting distribution of the ordinary least-squares (OLS) estimator in a linear simultaneous equations model. In simple static and dynamic models 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 …rst-order asymptotic …ndings are re‡ected in …nite sample, taking into account non-existence of moments of the IV estimator. 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).