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Health, Children, and Elderly Living Arrangements: A Multiperiod-Multinomial Probit Model with Unobserved Heterogeneity and Autocorrelated Errors

In: Topics in the Economics of Aging

Author

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  • Axel Borsch-Supan
  • Vassilis Hajivassiliou
  • Laurence J. Kotlikoff

Abstract

This paper develops a general multiperiod-multinomial probit model for panel data to estimate the living arrangements of the elderly. The model has the following features: (a) In each period choices do not necessarily obey the assumption of independence of irrelevant alternatives. (b) Unobserved person-specific attributes are treated as random effects. These random effects may also be correlated across alternatives. (c) In addition, unobserved choice-specific utility components may persist over some time, creating an autoregressive and/or heteroscedastic error structure. The model is estimated by simulating the choice probabilities in the likelihood function. We examine several variants of the specification of the correlation structure and investigate the extent the biases created by ignoring intertemporal correlations.
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Suggested Citation

  • Axel Borsch-Supan & Vassilis Hajivassiliou & Laurence J. Kotlikoff, 1992. "Health, Children, and Elderly Living Arrangements: A Multiperiod-Multinomial Probit Model with Unobserved Heterogeneity and Autocorrelated Errors," NBER Chapters,in: Topics in the Economics of Aging, pages 79-108 National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberch:7099
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    1. Vassilis A. Hajivassiliou & Daniel McFadden, 1990. "The Method of Simulated Scores for the Estimation of LDV Models with an Application to External Debt Crisis," Cowles Foundation Discussion Papers 967, Cowles Foundation for Research in Economics, Yale University.
    2. Laurence J. Kotlikoff & John N. Morris, 1989. "How Much Care Do the Aged Receive from Their Children? A Bimodal Picture of Contact and Assistance," NBER Chapters,in: The Economics of Aging, pages 151-176 National Bureau of Economic Research, Inc.
    3. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    4. Vassilis A. Hajivassiliou & Daniel L. McFadden, 1998. "The Method of Simulated Scores for the Estimation of LDV Models," Econometrica, Econometric Society, vol. 66(4), pages 863-896, July.
    5. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    6. Langdon, M. G., 1984. "Methods of determining choice probability in utility maximising multiple alternative models," Transportation Research Part B: Methodological, Elsevier, vol. 18(3), pages 209-234, June.
    7. Chamberlain, Gary, 1984. "Panel data," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 22, pages 1247-1318 Elsevier.
    8. Borsch-Supan, Axel, 1986. "Household formation, housing prices, and public policy impacts," Journal of Public Economics, Elsevier, vol. 30(2), pages 145-164, July.
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