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ON EFFICIENCY GAINS FROM MULTIPLE INCOMPLETE SUBSAMPLES
Published online by Cambridge University Press: 04 September 2019
Abstract
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Cost-effective survey methods such as multi(R)-phase sampling typically generate samples that are collections of monotonic subsamples, i.e., the variables observed for the units in subsample r are also observed for the units in subsample r + 1 for r = 1,…,R – 1. These subsamples represent subpopulations that can be systematically different if the selection of a unit in each phase of sampling depends on the observed variables for that unit from past phases. Our article is about optimally combining all the subsamples for the efficient estimation of a finite dimensional parameter defined by moment restrictions on a generic target population that is an arbitrary union of these subpopulations. Only the R-th subsample is assumed to contain all the variables that are arguments of the moment function. Semiparametric efficiency bounds for estimation are obtained under a unified framework, allowing for full generality of the selection on observables in the sampling design. Contribution of each subsample toward efficient estimation is analyzed; and this turns out to differ fundamentally from that in setups where the same collection of subsamples is instead generated unplanned by unknown sampling. Uniquely, our setup enables all the subsamples to contribute to the efficient estimation for all the target populations, which we show is not possible in other setups. Efficient estimation is standard. Simulation evidence of substantive efficiency gains from using all the subsamples is provided for all the targets.
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Footnotes
I am very much grateful to the editor P.C.B. Phillips, the co-editor P. Guggenberger and three anonymous referees for their detailed insightful comments. The article was circulated before as “A Note on Efficiency Gains from Multiple Incomplete Subsamples” but the title was modified at the suggestion of the editor. Previous versions of the article, some of which are available on the author’s webpage, benefitted from the helpful comments of A. Prokhorov, C. Muris, D. Guilkey, D. Frazier, E. Renault, F. Lange, J. Hill, J. Haushofer, J. MacKinnon, J. Wooldridge, M. Carrasco, M. Chemin, P. Saha Chaudhuri, S.J. Lee, and V. Zinde-Walsh, the seminar participants at Brown, Concordia, McGill (Econ and Biostat), Queen’s, U. Canterbury, U. Montreal, U. New South Wales, UNC Chapel Hill, U. Sydney, West Virginia University and the Midwest Econometrics Group meetings (2013).
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