Animations
Below, program files with extension swf can be downloaded. These should be run by the VLC media player or by Flashplayer software. Then they reveal 3D phenomena, related to two publications, by playing 2D movies.
For the article (jointly with Jerzy Niemczyk) Comparing the asymptotic and empirical (un)conditional distributions of OLS and IV in a linear static simultaneous equation (2012) published in the Journal of Computational Statistics & Data Analysis Vol.56, pp. 3567 - 3586, the following programs animate coefficient estimator densities (each based on 100,000 replications) for single regressor models with simultaneity correlation values -0.6, -0.4, -0.2, -0.1, 0, 0.1, 0.2, 0.4, 0.6 respectively. Cases covered are:
OLS (asymptotic/actual, conditional/unconditional), n=20(5)100, 100(10)300: denOLS.swf
IV (asymptotic, actual-conditional, actual-unconditional):
instrument strength correlation values 0.7(-0.025)0.025: n=50 denIVstrong50.swf; n=200 denIVstrong200.swf
instrument weakness correlation values 0.2(-0.005)0.005: n=50 denIVweak50.swf; n=200 denIVweak200.swf
For the article (jointly with Jerzy Niemczyk) On the limiting and empirical distribution of IV estimators when some of the instruments are actually endogenous (2014), pp. 425-490, published in: Advances in Econometrics, Volume 33; Essays in Honor of Peter C.B. Phillips (Eds. Yoosoon Chang, Thomas B. Fomby, Joon Y. Park), Emerald Group Publishing Limited (Bingley, UK), programs can be downloaded which animate various aspects the distribution of IV and OLS estimators. These are:
In single regressor models using just one (in)valid instrument:
Coefficient estimator densities (10,000 replications) for simultaneity correlation values 0, 0.3, 0.5 and instrument (in)validity correlation values -0.2, 0, 0.2, with:
instrument strength correlation values 0.7(-0.025)0.025: n=25 denInvIVst25.swf; n=100 denInvIVst100.swf
instrument weakness correlation values 0.2(-0.005)0.005: n=25 denInvIVwk25.swf; n=100 denInvIVwk100.swf
Accuracy of standard asymptotic approximations for instrument (in)validity correlation values 0, 0.1, 0.3, 0.6 and n=20,...,500: Figure5.swf
Absolute estimation errors OLS/IV for instrument (in)validity correlation values 0, 0.1, 0.3, 0.6 and n=20,...,500: Figure6.swf
In single regressor models using two instruments, one (in)valid and the other one valid:
Coefficient estimator densities (10,000 replications) for simultaneity correlation values 0, 0.3, 0.5 and instrument (in)validity correlation values -0.2, 0, 0.2, with:
instrument strength correlation values 0.7(-0.025)0.025: n=25 denInvGIVst25.swf; n=100 denInvGIVst100.swf
instrument weakness correlation values 0.2(-0.005)0.005: n=25 denInvGIVwk25.swf; n=100 denInvGIVst100.swf
Accuracy of standard asymptotic approximations for instrument (in)validity correlation values 0, 0.1, 0.3, 0.6 and n=20,...,500: Figure11.swf (published figure wrongly suggests l=1)
Absolute estimation errors OLS/IV for instrument (in)validity correlation values 0, 0.1, 0.3, 0.6 and n=20,...,500: Figure12.swf (published figure wrongly suggests l=1)