02159cam a22002537 4500001000600000003000500006005001700011008004100028100002300069245010200092260006600194490005100260500001500311520113100326530006101457538007201518538003601590690005701626700002101683710004201704830008601746856003701832856003601869t0150NBER20171212011210.0171212s1995 mau||||fs|||| 000 0 eng d1 aAngrist, Joshua D.10aSplit Sample Instrumental Variablesh[electronic resource] /cJoshua D. Angrist, Alan B. Krueger. aCambridge, Mass.bNational Bureau of Economic Researchc1995.1 aNBER technical working paper seriesvno. t0150 aJune 1995.3 aInstrumental Variables (IV) estimates tend to be biased in the same direction as Ordinary Least Squares (OLS) in finite samples if the instruments are weak. To address this problem we propose a new IV estimator which we call Split Sample Instrumental Variables (SSIV). SSIV works as follows: we randomly split the sample in half, and use one half of the sample to estimate parameters of the first-stage equation. We then use these estimated first-stage parameters to construct fitted values and second-stage parameter estimates using data from the other half sample. SSIV is biased toward zero, rather than toward the plim of the OLS estimate. However, an unbiased estimate of the attenuation bias of SSIV can be calculated. We us this estimate of the attenutation bias to derive an estimator that is asymptotically unbiased as the number of instruments tends to infinity, holding the number of observations per instrument fixed. We label this new estimator Unbiased Split Sample Instrumental Variables (USSIV). We apply SSIV and USSIV to the data used by Angrist and Krueger (1991) to estimate the payoff to education. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC30 - General2Journal of Economic Literature class.1 aKrueger, Alan B.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0150.4 uhttp://www.nber.org/papers/t015041uhttp://dx.doi.org/10.3386/t0150