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The Variances of Regression Coefficient Estimates Using Aggregate Data

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  • Roy E. Welsch
  • Edwin Kuh

Abstract

This paper considers the effect of aggregation on the variance of parameter estimates for a linear regression model with random coefficients and an additive error term. Aggregate and microvariances are compared and measures of relative efficiency are introduced. Necessary conditions for efficient aggregation procedures are obtained from the Theil aggregation weights and from measures of synchronization related to the work of Grunfeld and Griliches.

Suggested Citation

  • Roy E. Welsch & Edwin Kuh, 1974. "The Variances of Regression Coefficient Estimates Using Aggregate Data," NBER Working Papers 0060, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:0060
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    References listed on IDEAS

    as
    1. Edwin Kuh, 1974. "An Essay on Aggregation Theory and Practice," Palgrave Macmillan Books, in: Willy Sellekaerts (ed.), Econometrics and Economic Theory, chapter 3, pages 57-99, Palgrave Macmillan.
    2. Aigner, Dennis J & Goldfeld, Stephen M, 1974. "Estimation and Prediction from Aggregate Data when Aggregates are Measured More Accurately than Their Components," Econometrica, Econometric Society, vol. 42(1), pages 113-134, January.
    3. Swamy, P A V B & Arora, S S, 1972. "The Exact Finite Sample Properties of the Estimators of Coefficients in the Error Components Regression Models," Econometrica, Econometric Society, vol. 40(2), pages 261-275, March.
    4. Swamy, P A V B, 1970. "Efficient Inference in a Random Coefficient Regression Model," Econometrica, Econometric Society, vol. 38(2), pages 311-323, March.
    5. Aigner, D.J. & Goldfeld, S.M., 1974. "Estimation and prediction from aggregate data when aggregates are measured more accurately than their components," LIDAM Reprints CORE 190, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Feige, Edgar L & Watts, Harold W, 1972. "An Investigation of the Consequences of Partial Aggregation of Micro-Economic Data," Econometrica, Econometric Society, vol. 40(2), pages 343-360, March.
    7. Amemiya, Takeshi, 1971. "The Estimation of the Variances in a Variance-Components Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 12(1), pages 1-13, February.
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