Abstract
This study estimates the effect of complementary private health insurance (PHI) on the use of health care. The empirical analysis focuses on an institutional setting in which empirical findings are still limited; namely on PHI covering co-payment for treatments that are only partly financed by a universal health care system. The analysis is based on Danish data recently collected specifically for this purpose, which makes identification strategies assuming selection on observables only, and on both observables and unobservables also, both plausible and possible. We find evidence of a substantial positive and significant effect of complementary PHI on the use of prescription medicine and chiropractic care, a smaller but significant effect on dental care, weaker indications of effects for physiotherapy and general practice, and finally that the use of hospital-based outpatient care is largely unaffected. This implies that complementary PHI is generally not simply a marker of a higher propensity to use health care but induces additional use of some health care services over and above what would be used in the absence of such coverage.
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Notes
If, for example, the universal health care system covers 60 % of a physiotherapy treatment worth EUR 50 and the remaining 40 % is financed by a co-payment—which may or may not be covered by complementary insurance—and complementary insurance induces three additional visits at EUR 50 over and above what would have been used in its absence, the presence of complementary insurance leaves the universal health care system with an additional expenditure of EUR 0.6 * 150 \(=\) 90.
This approach has also been examined in the current study, but most bounds were too wide to be of any value.
Conversions from DKK to EUR were undertaken using the March 2011 average exchange rate of 745.74. (Danske Bank 2011).
The Danish Health Interview Survey (in Danish: Sundhed og Sygelighed i Danmark) contains information on private health insurance coverage and health care use in the Danish population. However, the level of detail of the information on private health insurance coverage is considerably lower than that of the data used here.
Based on the observed pattern, one might speculate that it is easier to remember visits for which a co-payment was made, sometimes perhaps even more visits than actually took place.
Probability weights are defined as the inverse of the probability that the individual under consideration was sampled from the population, i.e. the number of individuals in the population that each sampled respondent represents.
We perform a sensitivity analysis to check whether excluding passive individuals or classifying them as being insured changes the results substantially.
The choice of dummy variables indicating whether any use took place is motivated by the fact that the main choice that individuals face is whether to see a given health care provider or not, while further visits are, to a large extent, beyond their control (Barros et al. 2008; Gerfin and Schellhorn 2006). Moreover, a dummy variable captures the majority of the variation in outcomes, due to there being a large number of zeros and ones in the number of contacts.
All complementary insurance plans cover a maximum of DKK 360/USD 68 for single focal glasses or sunglasses, DKK 680/USD 128 for multifocal glasses and DKK 38/USD 7 per month for contact lenses (Health Insurance ’danmark’ 2010a). This is almost half the premium for complementary insurance coverage.
We have also estimated the models using univariate probit models, and the results are very similar to the matching results, indicating that functional form assumptions are not a problem. However, these are not reported, due to considerations of space.
A related estimator is the two-stage least squares estimator, but due to the discrete nature of both treatment and outcomes this will at best be an approximation.
The propensity score matching estimator was implemented using version 3.1.5 of the ‘psmatch2’ module written by Leuven and Sianesi (2003).
Sensitivity analyses, which are available from the corresponding author upon request, showed that the results are insensitive to reducing the bandwidth to 0.02 and increasing it to 0.06 and 0.08, respectively.
The average treatment effects for the treated are very similar and are hence not presented.
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Acknowledgments
The collection of the data used in the article was supported financially by the Danish Health Insurance Foundation (Helsefonden). The paper has benefitted greatly from discussions with Kjeld Møller Pedersen, Tor Iversen, Terkel Christiansen, Kristian Bolin, Lars Peter Østerdal, and participants in the 2010 Nordic Health Economists’ Study Group Meeting in Umeå, the 2011 Danish Symposium in Applied Statistics in Copenhagen and the 8th World Congress on Health Economics (IHEA), 2011, in Toronto. We also gratefully acknowledge the comments of two anonymous reviewers. Any errors are the responsibility of the authors.
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Appendices
Appendix 1: Regression results
This appendix contains the regression results underlying the parametric models for which treatment effects are presented in Table 5.
See Table 6.
Appendix 2: Assessment of matching quality and common support
This appendix contains some diagnostics of matching quality for the propensity score matching estimator.
Propensity scores for treated and non-treated, n \(=\) 4362
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Kiil, A., Arendt, J.N. The effect of complementary private health insurance on the use of health care services. Int J Health Econ Manag. 17, 1–27 (2017). https://doi.org/10.1007/s10754-016-9195-3
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DOI: https://doi.org/10.1007/s10754-016-9195-3
Keywords
- Private health insurance
- Moral hazard
- Health care utilization
- Treatment effects
- Parametric estimators
- Propensity score matching