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Charles R. Nelson, Richard Startz, The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument is a Poor One, The Journal of Business, Vol. 63, No. 1, Part 2: A Conference in Honor of Merton H. Miller's Contributions to Finance and Economics (Jan., 1990), pp. S125-S140
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Nelson et al. (1990) studied this question.
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