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Linear regression with an estimated regressor: applications to aggregate indicators of economic development

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  • Lingsheng Meng

    (Tsinghua University)

  • Binzhen Wu

    (Tsinghua University)

  • Zhaoguo Zhan

    (Tsinghua University)

Abstract

This study examines the consequences of using an estimated aggregate measure as an explanatory variable in linear regression. We show that neglecting the seemingly small sampling error in the estimated regressor could severely contaminate the estimates. We propose a simple statistical framework to account for the error. In particular, we apply our analysis to two aggregate indicators of economic development, the Gini coefficient and sex ratio. Our findings suggest that the impact of the estimated regressor could be substantially underestimated, when the sampling error is not accounted for.

Suggested Citation

  • Lingsheng Meng & Binzhen Wu & Zhaoguo Zhan, 2016. "Linear regression with an estimated regressor: applications to aggregate indicators of economic development," Empirical Economics, Springer, vol. 50(2), pages 299-316, March.
    • Handle: RePEc:spr:empeco:v:50:y:2016:i:2:d:10.1007_s00181-015-0941-z
    DOI: 10.1007/s00181-015-0941-z
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    2. Mochen Yang & Edward McFowland & Gordon Burtch & Gediminas Adomavicius, 2022. "Achieving Reliable Causal Inference with Data-Mined Variables: A Random Forest Approach to the Measurement Error Problem," INFORMS Joural on Data Science, INFORMS, vol. 1(2), pages 138-155, October.
    3. Kahsay, Goytom Abraha & Medhin, Haileselassie, 2020. "Leader turnover and forest management outcomes: Micro-level evidence from Ethiopia," World Development, Elsevier, vol. 127(C).
    4. Mochen Yang & Edward McFowland III & Gordon Burtch & Gediminas Adomavicius, 2020. "Achieving Reliable Causal Inference with Data-Mined Variables: A Random Forest Approach to the Measurement Error Problem," Papers 2012.10790, arXiv.org.
    5. Chen, Yuanyuan & Yuan, Meng & Zhang, Min, 2023. "Income inequality and educational expenditures on children: Evidence from the China Family Panel Studies," China Economic Review, Elsevier, vol. 78(C).

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    More about this item

    Keywords

    Estimated regressor; Sampling error; Gini; Sex ratio; Inequality;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • D6 - Microeconomics - - Welfare Economics

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