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Reduced-Dimension Control Regression

  • John Galbraith

    ()

  • Victoria Zinde-Walsh

    ()

A model to investigate the relationship between one variable and another usually requires controls for numerous other effects which are not constant across the sample; where the model omits some elements of the true process, estimates of parameters of interest will typically be inconsistent. Here we investigate conditions under which, with a set of potential controls which is large (possibly infinite), orthogonal transformations of a subset of potential controls can nonetheless be used in a parsimonious regression involving a reduced number of orthogonal components (the ‘reduced-dimension control regression’), to produce consistent (and asymptotically normal, given further restrictions) estimates of a parameter of interest, in a general setting. We examine selection of the particular orthogonal directions, using a new criterion which takes into account both the magnitude of the eigenvalue and the correlation of the eigenvector with the variable of interest. Simulation experiments show good finite-sample performance of the method.

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File URL: http://www.mcgill.ca/files/economics/reduceddimensioncontrol.pdf
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Paper provided by McGill University, Department of Economics in its series Departmental Working Papers with number 2006-17.

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Length: 29 pages
Date of creation: Aug 2006
Date of revision:
Handle: RePEc:mcl:mclwop:2006-17
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