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Dynamic modelling of long-term care decisions

Abstract

This paper describes and analyzes research on the dynamics of long-term care and the policy relevance of identifying the sources of persistence in caregiving arrangements (including the effect of dynamics on parameter estimates, implications for family welfare, parent welfare, child welfare, and cost of government programs). We discuss sources and causes of observed persistence in caregiving arrangements including inertia/state dependence (confounded by unobserved heterogeneity) and costs of changing caregivers. We comment on causes of dynamics including learning/human capital accumulation; burnout; and game-playing. We suggest how to deal with endogenous geography; dynamics in discrete and continuous choices; and equilibrium issues (multiple equilibria, dynamic equilibria). We also present an overview of commonly used longitudinal data sets and evaluate their relative advantages/disadvantages. We also discuss other data issues related to noisy measures of wealth and family structure. Finally, we suggest some methods to handle econometric problems such as endogeneous geography.

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Notes

  1. We abstract away from discrete elements of y jt which imply a derivative doesn’t exist.

  2. These papers may employ different distributional assumptions for unobserved heterogeneity; how and whether it enters the initial conditions is not the focus of this paper.

  3. Gemici (2011) is a very simple special case.

  4. Mazzocco (2004) provides some evidence supportive of this assumption.

  5. Some of the time-varying child characteristics may be endogenous (such as work status and geographical distance).

  6. An exception might be ending a relationship with a particular formal care provider.

  7. There is no empirical version of Hart and Tirole (1988) or dynamic version of Lundberg and Pollak (1993) or Heidemann and Stern (1999) implying it may be too demanding.

  8. Note that a model like Bernheim, Schleifer, and Summers (1985) would have implications for δ having nothing to do with complementarity/ substitutability. If the reaction of other children to one who is providing a lot of care is to compete and offer more care, then δ > 0; if instead, the other children give up, then δ < 0.

  9. Exceptions are Mazzocco (2007) and Rainer and Siedler (2009). But Mazzocco (2007) is about savings behavior and risk preferences within a family, and Rainer and Siedler (2009), though extremely relevant to informal care, is not empirical.

  10. Exceptions include Sloan et al. (1997), Pezzin and Schone (1999b), Checkovich and Stern (2002), Van Houtven and Norton (2004), and Byrne et al. (2009).

  11. We ignore some other terms irrelevant to the discussion.

  12. Hill (2006) also finds unusual variation in changes in assets in HRS.

  13. Skira (2012), for example, uses potential caregivers in a study of caregiver behavior.

  14. Denmark, Sweden, Austria, France, Germany, Switzerland, Belgium, the Netherlands, Spain, Italy, and Greece were involved in 2004; Israel, the Czech Republic, Poland, and Ireland were added in wave 2.

  15. Many papers have provided extensions including Viitanen (2005), Heitmuller (2007), Kyung Do (2008), Casado-Marín et al. (2011), and Witvorapong (2011).

  16. We adjust the notation in some papers so it is compatible with the rest of this paper.

  17. Witvorapong (2011) expands the set of long term care choices to interact informal and formal care with living alone and living with a child.

  18. In static models, Byrne et al. (2009) model care in the same way as the structural model; Van Houtven and Norton (2004) model health in the same way as in GG but do not estimate a health equation; and Bonsang and Bordone (2013) find a negative effect.

  19. In the empirical search literature, it is difficult to identify job offer probabilities from the probability of rejecting received wage offers, even when accepted wage offers are observed. In the theoretical job search literature, the job offer arrival rate has to be higher when not employed than when employed to generate endogenous transitions from jobs (e.g., Rogerson, Shimer, and Wright, 2005). Given the data moments Sk uses to estimate her model, she, in fact, faces the same problem. However, while this is an important econometric point, the economic point can be generalized to say that caregiving significantly reduces labor market opportunities, whether they be through lower offer probabilities or lower offers.

  20. One might think that Rainer and Siedler (2009) implies that distance, an “exogenous” simulated variable, is endogenous because the oldest child behaves strategically when choosing location. But behavior depends only on the number of children in the family, i.e., not on the endogenous variables or errors when the family has to make a caregiving decision.

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Sovinsky, M., Stern, S. Dynamic modelling of long-term care decisions. Rev Econ Household 14, 463–488 (2016). https://doi.org/10.1007/s11150-013-9236-3

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Keywords

  • Informal Care
  • Unobserved Heterogeneity
  • Care Arrangement
  • Duration Dependence
  • British Household Panel Survey