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Reduced-Dimension Control Regression

Author

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  • 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.

Suggested Citation

  • John Galbraith & Victoria Zinde-Walsh, 2006. "Reduced-Dimension Control Regression," Departmental Working Papers 2006-17, McGill University, Department of Economics.
    • Handle: RePEc:mcl:mclwop:2006-17
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    File URL: http://www.mcgill.ca/files/economics/reduceddimensioncontrol.pdf
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    Cited by:

    1. Anatolyev, Stanislav, 2012. "Inference in regression models with many regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 368-382.
    2. Stanislav Anatolyev, 2007. "Inference about predictive ability when there are many predictors," Working Papers w0096, Center for Economic and Financial Research (CEFIR).

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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