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Testing the red herring hypothesis on an aggregated level: ageing, time-to-death and care costs for older people in Sweden

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In this paper we test the ‘red herring’ hypothesis for expenditures on long-term care (LTC). The main contribution of this paper is to assess the ‘red herring’ hypothesis by using the probability of dying as a measure for time-to-death (TTD). In addition, we implement models that allow for age-specific TTD effects on LTC utilization as well as sex-specific effects. We also focus on total, institutional and domiciliary LTC separately. For our analysis we use high quality administrative data from Sweden. Our analysis is based on fixed effects estimates. We use our findings to project future LTC expenditures and show that, although TTD is a relevant predictor, age itself remains the main driver of LTC expenditures.

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  1. Data on LTC expenditures is available at

  2. See "Appendix 1".

  3. Data provided by Statistics Sweden can be downloaded at

  4. As already mentioned, some 4 % of total costs are covered by user charges. These are included in our cost variables so that these reflect the actual total costs of LTC for each individual in the publicly funded system.

  5. For a detailed variable description see in "Appendix 2".

  6. The pattern of lower probabilities of dying for higher age groups, as seen in Table 1, is simply a result of the variables being rescaled, as described above.

  7. The 65+ population changes its municipality with a probability of around 0.011, a figure that is even lower (0.007) for the population aged 80+ [3].

  8. A Hausman test supports the hypothesis that the consistency of a Random Effects estimate can be rejected.

  9. We also estimate specifications where both contemporary and next year’s mortality are included. Wald tests do not reject the null hypothesis of the equality of both coefficients, suggesting that they control for the same mechanism influencing LTC costs. Therefore, we regard aggregation of both variables to be an appropriate way to control for the overall effect using just the aggregated variable—TTD65+.

  10. Descriptive statistics are provided in "Appendix 3".

  11. To evaluate to what extent the coefficients of sex-specific TTD are reliable and not a result of colinearity due to the inclusion of many TTD variables, we run single regressions with just one specific TTD variable included. A reason for such a problem could be comorbidity of very old people, which would not allow identifying the TTD effects separately for both sexes. However, these estimates prove the findings for the complete specification being very similar both in terms of economic relevance and statistical significance.

  12. The formula for cost increase per life year is provided in “Appendix 6”.

  13. The pattern is similar if we use sex-specific estimates ("Appendices 7, 8").


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We would like to thank participants of different events for excellent comments on previous versions of this paper: the Berlin Network of Labour Market Research, the 2010 NHESG conference in Umea, the 2010 DIBOGS Workshop in Neuss, the Actuarial Research Seminar at Cass Business School and the 2011 iHEA Congress in Toronto, participants of a research colloquium at the DZA in Berlin.

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Correspondence to Florian Klohn.


Appendix 1

See Table 6.

Table 6 Comparison of municipalities (not) providing health care in 2008

Appendix 2

See Table 7.

Table 7 Variable definitions

Appendix 3

See Table 8.

Table 8 Sex specific summary statistics

Appendix 4

See Table 9.

Table 9 Sex-specific institutional LTC expenditures

Appendix 5

See Table 10.

Table 10 Sex-specific domiciliary LTC expenditures

Appendix 6: Changes in cost increase per 65+ life year

$$ \Delta {\text{LTC}}_{{it}} = \left\{ {\begin{array}{*{20}c} {\sum\nolimits_{{k = 65}}^{\infty } {\left( {\alpha _{j} + \beta _{j}^{k} } \right)} \left( {\frac{{s_{{2008}}^{{k - 1}} }}{{\sum\nolimits_{{k = 65}}^{\infty } {s_{{2008}}^{{k - 1}} } }} - \frac{{s_{{2008}}^{k} }}{{\sum\nolimits_{{k = 65}}^{\infty } {s_{{2008}}^{k} } }}} \right) {\text{with}} \; j = i,} \hfill & {{\text{for }}i = 1,2} \hfill \\ {\sum\nolimits_{{k = 65}}^{\infty } {\left( {\left( {\alpha _{j} + \beta _{j}^{k} } \right)\left( {\frac{{s_{{2008}}^{{k - 1}} }}{{\sum\nolimits_{{k = 65}}^{\infty } {s_{{2008}}^{{k - 1}} } }} - \frac{{s_{{2008}}^{k} }}{{\sum\nolimits_{{k = 65}}^{\infty } {s_{{2008}}^{k} } }}} \right) + \delta _{k}^{j} \left( {\frac{{TTD_{{2008}}^{{k - 1}} }}{{\sum\nolimits_{{k = 65}}^{\infty } {s_{{2008}}^{{k - 1}} } }} - \frac{{TTD_{{2008}}^{k} }}{{\sum\nolimits_{{k = 65}}^{\infty } {s_{{2008}}^{k} } }}} \right)} \right)} {\text{with}} \quad j = i,} \hfill & {{\text{for }}i = 3} \hfill \\ {\frac{{\alpha _{j} + \sum\nolimits_{{k = 65}}^{\infty } {\left( {\alpha _{j} + \beta _{j}^{k} } \right)} s_{{2008}}^{{k - 1}} }}{{\sum\nolimits_{{k = 65}}^{\infty } {s_{{2008}}^{{k - 1}} } }} - \frac{{\sum\nolimits_{{k = 65}}^{\infty } {\left( {\alpha _{j} + \beta _{j}^{k} } \right)} s_{{2008}}^{k} }}{{\sum\nolimits_{{k = 65}}^{\infty } {s_{{2008}}^{k} } }} {\text{with}} \; j = 1,} \hfill & {{\text{for }}i = 4} \hfill \\ \end{array} } \right. $$

Appendix 7

See Fig. 5.

Fig. 5
figure 5

Total cost increase per capita associated with an increase of life expectancy by 1 year (various scenarios based on sex-specific estimates)

Appendix 8

See Fig. 6.

Fig. 6
figure 6

Total cost increase per capita and per life year associated with an increase of life expectancy by 1 year (various scenarios based on sex-specific estimates)

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Karlsson, M., Klohn, F. Testing the red herring hypothesis on an aggregated level: ageing, time-to-death and care costs for older people in Sweden. Eur J Health Econ 15, 533–551 (2014).

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