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Linear Regressions, Shorts to Long

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  • KITAGAWA, Toru
  • SAWADA, Masayuki

Abstract

We study the identification problem of the linear long regression coefficients by data combination. Unlike the usual data combination problem, we consider combining multiple short regressions of the same outcome with different regressors. For this conceptually novel problem, we provide partial identification results for the long regression coefficients under a restriction on the unknown correlation structure. Specifically, we employ an elliptic constraint from the relations among the explained variations of the regressions to induce the bounds.

Suggested Citation

  • KITAGAWA, Toru & SAWADA, Masayuki, 2023. "Linear Regressions, Shorts to Long," Discussion Paper Series 747, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hit:hituec:747
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    File URL: https://hermes-ir.lib.hit-u.ac.jp/hermes/ir/re/80139/DP747.pdf
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    References listed on IDEAS

    as
    1. Guildo W. Imbens, 2003. "Sensitivity to Exogeneity Assumptions in Program Evaluation," American Economic Review, American Economic Association, vol. 93(2), pages 126-132, May.
    2. Krauth Brian, 2016. "Bounding a Linear Causal Effect Using Relative Correlation Restrictions," Journal of Econometric Methods, De Gruyter, vol. 5(1), pages 117-141, January.
    3. Carlos Cinelli & Chad Hazlett, 2020. "Making sense of sensitivity: extending omitted variable bias," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(1), pages 39-67, February.
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    Keywords

    Data combination; Linear regression; Elliptic constraint;
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