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Least Square Linear Prediction with Two-Sample Data

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  • David Pacini

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Abstract

This paper investigates the identification and estimation of the least square linear predictor for the conditional expectation of an outcome variable Y given covariates (X;Z0) from data consisting of two independent random samples; the first sample contains replications of the variables (Y;Z0) but not X, while the second sample contains replications of (X;Z0) but not Y . The contribution is to characterize the identified set of the least square linear predictor when no assumption on the joint distribution of (Y;X;Z0), except for the existence of second order moments, is imposed. We show that the identified set is not a singleton, so the least square linear predictor of interest is set identified. The characterization is used to construct a sample analog estimator of the identified set. The asymptotic properties of the estimator are established and its implementation is illustrated via Monte Carlo exercises.

Suggested Citation

  • David Pacini, 2012. "Least Square Linear Prediction with Two-Sample Data," Bristol Economics Discussion Papers 12/631, Department of Economics, University of Bristol, UK.
  • Handle: RePEc:bri:uobdis:12/631
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    More about this item

    Keywords

    Network Identification; Least Square Linear Prediction; Two samples;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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