NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator

Charles R. Nelson, Richard Startz

NBER Technical Working Paper No. 68
Issued in September 1988
NBER Program(s):   ME

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.

download in pdf format
   (936 K)

email paper

This paper is available as PDF (936 K) or via email.

Machine-readable bibliographic record - MARC, RIS, BibTeX

Document Object Identifier (DOI): 10.3386/t0068

Published: Journal of Business, January 1990.

Users who downloaded this paper also downloaded these:
Nelson and Startz t0069 The Distribution of the Instrumental Variables Estimator and Its t-RatioWhen the Instrument is a Poor One
Staiger and Stock t0151 Instrumental Variables Regression with Weak Instruments
Heckman t0184 Randomization as an Instrumental Variable
 
Publications
Activities
Meetings
Data
People
About

Support
National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email: info@nber.org

Contact Us