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Consistent Estimation of Regression Models with Incompletely Observed Exogenous Variables

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  • Theodore E. Nijman
  • Franz C. Palm

Abstract

We consider consistent estimation of regression models in which the exogenous variables are incompletely observed assuming that the response mechanism is random. In the literature on imputed data, several estimators have been proposed which are based on approximations substituted for the missing data. We discuss conditions under which these proxy variables estimators are asymptotically more efficient than the estimator based on complete observations and we show how an optimal proxy variables estimator can be obtained. For simple models, some proxy variables estimators are almost as efficient as the Gaussian maximum likelihood (ML) estimator and sometimes more efficient than the pseudo ML estimator.

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  • Theodore E. Nijman & Franz C. Palm, 1988. "Consistent Estimation of Regression Models with Incompletely Observed Exogenous Variables," Annals of Economics and Statistics, GENES, issue 12, pages 151-175.
    • Handle: RePEc:adr:anecst:y:1988:i:12:p:151-175
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    1. Nijman, T E & Palm, F C, 1986. "The Construction and Use of Approximations for Missing Quarterly Observations: A Model-based Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 47-58, January.
    2. Eijffinger, S.C.W., 1987. "The determinants of the currencies within the European Monetary System," Other publications TiSEM e398a10d-9cec-435e-a488-0, Tilburg University, School of Economics and Management.
    3. Palm, Franz C & Nijman, Theo E, 1984. "Missing Observations in the Dynamic Regression Model," Econometrica, Econometric Society, vol. 52(6), pages 1415-1435, November.
    4. Palm, F. C. & Nijman, T. E., 1982. "Linear regression using both temporally aggregated and temporally disaggregated data," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 333-343, August.
    5. Griliches, Zvi, 1986. "Economic data issues," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 25, pages 1465-1514, Elsevier.
    6. Denis Conniffe, 1983. "Small-Sample Properties of Estimators of Regression Coefficients Given a Common Pattern of Missing Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 111-120.
    7. Dagenais, Marcel G., 1973. "The use of incomplete observations in multiple regression analysis : A generalized least squares approach," Journal of Econometrics, Elsevier, vol. 1(4), pages 317-328, December.
    8. J. C. G. Boot & W. Feibes & J. H. C. Lisman, 1967. "Further Methods of Derivation of Quarterly Figures from Annual Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 16(1), pages 65-75, March.
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    1. Feijoo, Santiago Rodriguez & Caro, Alejandro Rodriguez & Quintana, Delia Davila, 2003. "Methods for quarterly disaggregation without indicators; a comparative study using simulation," Computational Statistics & Data Analysis, Elsevier, vol. 43(1), pages 63-78, May.

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