Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2006-09-18 Number: 06-078/4 Author-Name: Jan F. Kiviet Author-Email: firstname.lastname@example.org Author-Workplace-Name: Universiteit van Amsterdam Author-Name: Jerzy Niemczyk Author-Email: email@example.com Author-Workplace-Name: Universiteit van Amsterdam Title: The Asymptotic and Finite Sample Distributions of OLS and Simple IV in Simultaneous Equations Abstract: This discussion paper led to a publication in 'Computational Statistics & Data Analysis' 51(7) 3296-318.
In practice structural equations are often estimated by least-squares, thus neglecting 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 find 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 efficiency 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 sample, taking into account non-existence of moments of the IV estimator. By dynamic visualization techniques we enable to appreciate any differences in efficiency over a parameter space of a much higher dimension than just two, viz. in colored animated image sequences (which are not very effective in print, but much more so in live-on-screen projection). Classification-JEL: C13; C15; C30 Keywords: efficiency of an inconsistent estimator; invalid instruments; simultaneity bias; weak instruments; 4D diagrams File-Url: http://papers.tinbergen.nl/06078.pdf File-Format: application/pdf File-Size: 604713 bytes Handle: RePEc:tin:wpaper:20060078