TY - JOUR
AU - Nelson,Charles R.
AU - Startz,Richard
TI - Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator
JF - National Bureau of Economic Research Technical Working Paper Series
VL - No. 68
PY - 1988
Y2 - September 1988
DO - 10.3386/t0068
UR - http://www.nber.org/papers/t0068
L1 - http://www.nber.org/papers/t0068.pdf
N1 - Author contact info:
Charles Nelson
Department of Economics
University of Washington
Seattle, WA 93195
E-Mail: cnelson@u.washington.edu
Richard Startz
Department of Economics, Box 353330
University of Washington
Seattle, WA 98195-3330
Tel: 206-543-8172
E-Mail: startz@ucsb.edu
AB - New results on the exact small sample distribution of the instrumental variable estimator are presented by studying an important special case. The exact closed forms for the probability density and cumulative distribution functions are given. There are a number of surprising findings. The small sample distribution is bimodal. with a point of zero probability mass. As the asymptotic variance grows large, the true distribution becomes concentrated around this point of zero mass. The central tendency of the estimator may be closer to the biased least squares estimator than it is to the true parameter value. The first and second moments of the IV estimator are both infinite. In the case in which least squares is biased upwards, and most of the mass of the IV estimator lies to the right of the true parameter, the mean of the IV estimator is infinitely negative. The difference between the true distribution and the normal asymptotic approximation depends on the ratio of the asymptotic variance to a parameter related to the correlation between the regressor and the regression, error. In particular, when the instrument is poorly correlated with the regressor, the asymptotic approximation to the distribution of the instrumental variable estimator will not be very accurate.
ER -