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Nonlinear relationship between health care expenditure and its determinants: a panel smooth transition regression model

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Abstract

This paper employs a panel of 16 OECD countries over the period 1975–2009 to reexamine the health care expenditure (HCE)-income relationship by considering a lagged ratio of public expenditures on health as the transition variable in panel smooth transition regression (PSTR) models. PSTR models can capture the heterogeneity of any individual country, provide more detailed information for policy makers of an individual government, and resolve the insufficient observations problem that frequently appears in annual country-level data. Our empirical results indicate that the relationship between HCE and its determinants, including income, time (trend), and age structure variables, is nonlinear and varies with time and across countries. The time (trend) variable—a proxy for technical progress in health care—has a non-linear impact on HCE. Ignoring the variables—technological change of health care and age structure of population—will result in over-estimates of the income elasticities of HCE. Moreover, HCE behaves as a necessity good, and the income elasticity increases when the five-period lagged ratio of public expenditures on health increases. Clearly, the ratio of government financing on health plays an important role in influencing HCE.

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Notes

  1. Some famous regime-switching models been developed for describing the nonlinear dynamic adjustment of economic variables, including the threshold autoregressive (TAR) model, Markov switching (MS) model (Hamilton 1990; Smith 2002), smooth transition autoregressive (STAR) model, and neural networks (NN) model. Essentially, the switching process of economic variables in the TAR or MS model is radical and discrete, which scarcely corresponds to the actual movement. In contrast, the STAR model and the STARX model both allow for smooth rather than discrete switching between regimes, and they can endogenously estimate the transition parameter and transition speed..

  2. They have introduced dynamic nonlinear panel models through the development of PLSTAR (panel logistic smooth transition auto-regression) models. For more details and discussions on the utility of PSTR models, see, for example, Colletaz and Hurlin (2006) and Fouquau et al. (2008).

  3. While some other variables may be specified as the transition variable, our concern is the ratio of public expenditures on health. Because fiscal deterioration in many European countries has been obvious for recent years, this may change the public expenditures on health, which further influences HCE.

  4. Note that the case m = 1 corresponds to a logistic PSTR model, and m = 2 refers to a logistic quadratic PSTR specification. For more details about PSTR model, see Fouquau et al. (2008).

  5. Hitris and Posnett (1992) argue that the use of health specific PPP to convert health spending provides a comparison of the real quantity of health care services purchased with a given expenditure.

  6. Although the time trend is not the only and perfect proxy of technology change, many studies have used it (e.g., Blomqvist and Carter 1997; Gerdtham and Löthgren 2000; Clemente et al. 2004; Di Matteo 2004). The time trend used in this study can stand for the technological progress of healthcare common to all individual countries. For example, the use of computers is helpful for reducing the production cost of health care and stimulating health expenditures. Some type of medical technology progress may lead to differential impacts on the health expenditures of individual countries. However, we cannot use these data for empirical estimation due to hard identification and incomplete available data. For example, patents and R&D expenditures are frequently used as the proxies of technology change (Popp 2001); however, the former is an under-representative one, and the latter has an incomplete data set of the sample countries. More importantly, the estimated coefficients of time trend vary with time and across countries, which is quietly different from the constant coefficient generated from traditional linear models.

  7. While Dreger and Reimers (2005) use life expectancy as a proxy for medical progress, there are no obvious differences between the life expectancy in the OECD countries. Moreover, Newhouse (1977) argues that health care price cannot be considered a relevant determinant of health care spending in Western countries because non-market rationing dominates. In addition, the data set of health care prices in our sample countries is quite incomplete. Thus, this paper excludes health care price indices as explanatory variables.

  8. In fact, we also conduct a second test of non-remaining linearity with direct effects in which the transition variable is used as an explanatory variable, and the result supports the fact that the lagged transition variable has no direct effect on the dependent variable.

  9. The public expenditures on health can take some different forms: public-paid premiums for private insurers, public-paid bills for private health providers, or public-financed health care.

  10. For more details, see Fouquau et al. (2008).

  11. This study employs a panel data set of 16 sample countries and 35 years to conduct empirical estimation. Thus, it is not easy to cover some other regressors due to incomplete data. For example, Hartwig (2008) uses only one country (Switzerland) to investigate whether a lower productivity growth in the health care sector contributes to the change of HCE. However, we have incomplete panel data of the productivity growth in the health care sector to estimate the PSTR models. In addition, some variables influencing HCE display an extremely stable time path and a little difference among the 16 sample countries, such as the mortality rates; therefore, they have insignificant effects on HCE. Moreover, the transition variable used in this study (i.e., ratio of public expenditures on health) has embodied the past information of omitted variables (e.g., mortality rates and productivity growth in health care sector). Thus, this study excludes them from the candidate regressors.

  12. We only display the results from the optimal estimation model; however, the remaining estimation results are available upon request.

  13. This paper also conducts the Hausman test to confirm whether there is an endogeneity problem in our specification of income-health model. The testing result shows that there is no endogeneity problem.

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Authors and Affiliations

  1. Department of International Business, Chung Yuan Christian University, No. 200, Chung Pei Rd., Chung Li, 320, Taiwan, ROC

    Po-Chin Wu & Shiao-Yen Liu

  2. Department of Tourism and Leisure Management, China University of Technology, 530, Sec. 3, Jhongshan Rd., Hukou Township, Hsinchu County, Taiwan, ROC

    Sheng-Chieh Pan

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  1. Po-Chin Wu
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  2. Shiao-Yen Liu
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  3. Sheng-Chieh Pan
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Correspondence to Po-Chin Wu.

Appendix

Appendix

See Table 5.

Table 5 Descriptive statistics and panel unit root test
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Wu, PC., Liu, SY. & Pan, SC. Nonlinear relationship between health care expenditure and its determinants: a panel smooth transition regression model. Empirica 41, 713–729 (2014). https://doi.org/10.1007/s10663-013-9233-z

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