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Reduced-Dimension Control Regression

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Author Info

  • John Galbraith

    ()

  • Victoria Zinde-Walsh

    ()

Abstract

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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Bibliographic Info

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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Cited by:
  1. Stanislav Anatolyev, 2009. "Inference in Regression Models with Many Regressors," Working Papers w0125, Center for Economic and Financial Research (CEFIR).
  2. Stanislav Anatolyev, 2007. "Inference about predictive ability when there are many predictors," Working Papers w0096, Center for Economic and Financial Research (CEFIR).

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