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Identification, Estimation and Testing in Panel Data Models with Attrition: The Role of the Missing at Random Assumption

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    Abstract

    This paper discusses identification, estimation and testing in panel data models with attrition. We focus on a situation which often occurs in the analysis of firms: Attrition (exit) is endogenous and depends on the outcomes of an observed stochastic process and the interest-parameters characterizing this process. Thus attrition is non-ignorable even if selection is based only on observed variables - that is, even if the missing items are missing at random (MAR). The likelihood function obtained by ignoring the attrition mechanism is a pseudo likelihood function. Assuming that the MAR condition holds, this paper establishes conditions for identification and consistent estimation based on the pseudo likelihood function. It is also shown that the MAR hypothesis has testable implications in many situations that are encountered in practice. Simulations suggest that in the case of the autoregressive model with random effects, the efficiency of the pseudo likelihood estimator (based on normality) is not much affected even by strong departures from normality. In a variety of simulation models, the pseudo likelihood estimator clearly outperforms the moment estimators - even when the latter are consistent.

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    File URL: http://www.ssb.no/a/publikasjoner/pdf/DP/dp-330.pdf
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    Bibliographic Info

    Paper provided by Research Department of Statistics Norway in its series Discussion Papers with number 330.

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    Date of creation: Sep 2002
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    Handle: RePEc:ssb:dispap:330

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    Keywords: Missing at random; non-ignorable attrition; unbalanced panel data; identification; pseudo likelihood; martingale.;

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    1. Arellano, Manuel & Bover, Olympia, 1995. "Another look at the instrumental variable estimation of error-components models," Journal of Econometrics, Elsevier, vol. 68(1), pages 29-51, July.
    2. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
    3. Richard Blundell & Steve Bond, 1995. "Initial conditions and moment restrictions in dynamic panel data models," IFS Working Papers W95/17, Institute for Fiscal Studies.
    4. Gourieroux Christian & Monfort Alain & Trognon A, 1981. "Pseudo maximum likelihood methods : theory," CEPREMAP Working Papers (Couverture Orange) 8129, CEPREMAP.
    5. John M. Abowd & Bruno Crepon & Francis Kramarz, 1997. "Moment Estimation with Attrition," NBER Technical Working Papers 0214, National Bureau of Economic Research, Inc.
    6. Hausman, Jerry A & Wise, David A, 1979. "Attrition Bias in Experimental and Panel Data: The Gary Income Maintenance Experiment," Econometrica, Econometric Society, vol. 47(2), pages 455-73, March.
    7. Ahn, Seung C. & Schmidt, Peter, 1995. "Efficient estimation of models for dynamic panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 5-27, July.
    8. Robert MOFFIT & John FITZGERALD & Peter GOTTSCHALK, 1999. "Sample Attrition in Panel Data: The Role of Selection on Observables," Annales d'Economie et de Statistique, ENSAE, issue 55-56, pages 129-152.
    9. Horowitz, J.L. & Manski, C.F., 1995. "Censoring of Outcomes and Regressors Due to Survey Nonresponse: Identification and estimation Using Weights and Imputations," Working Papers 95-12, University of Iowa, Department of Economics.
    10. Hahn, Jinyong, 1999. "How informative is the initial condition in the dynamic panel model with fixed effects?," Journal of Econometrics, Elsevier, vol. 93(2), pages 309-326, December.
    11. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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