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Stationarity and cointegration of health care expenditure and GDP: evidence from tests with smooth structural shifts

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Abstract

This paper studies stationarity and cointegration of healthcare expenditure (HE) and GDP for a sample of OECD countries. In particular, we employ newly developed unit root and cointegration tests which approximate an unknown number of smooth structural shifts in the low-frequency components of a Fourier expansion. The new unit root test indicates that HE and GDP are non-stationary. In the presence of a number of smooth shifts in the cointegration regression, our empirical results support the existence of stochastic comovement between HE and GDP in 14 out of 20 OECD countries. In addition, we examine the income elasticity of HE for the countries that we found cointegration relationship between HE and GDP. We found 13 out of 14 countries with income elasticity of HE higher than 1, which implies that health care is a luxury good.

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Notes

  1. In particular, see McCoskey and Selden (1998) and Gerdtham and Lothgren (2000). Their arguments are mainly based on well-known studies such as Perron (1989, 2006), Campos et al. (1996), Gregory and Hansen (1996a), and Leybourne and Newbold (2003).

  2. The long-run cointegration relationship between HE and GDP has been examined for states in the USA and groups of non-OECD countries in some recent research. See Wang and Rettenmaier (2007), Moscone and Tosetti (2010), and Baltagi et al. (2017). These recent studies investigate non-stationarity and cointegration based on panel-based tests while controlling for the cross-sectional dependence among panel units. These approaches provide rationales to understand the real-time situation that both HE and income among different states (or countries) could be affected by common shocks in economics.

  3. Recent researchers have developed unit root and cointegration tests whose deterministic component assumes smooth shifts rather than sharp breaks; see Leybourne et al. (1998), Kapetanios et al. (2003), Enders and Lee (2012a, b), and Banerjee et al. (2017).

  4. See also the discussion in Jewell et al. (2003).

  5. For more detail, see Pesavento (2004), Zivot (2000), and Lee et al. (2015).

  6. For example, the threshold cointegration test of Li and Lee (2010) extends the ADL test by including indicator functions reflecting a regime change.

  7. Using the same data period allows us to avoid selecting an arbitrary time span and to compare previous findings to ours. Although an updated version of the Health Data File is available, it has not been considered in the literature due to lack of consistency in the long time series. For example, Carrion-i-Silvestre (2005) points out that the updated data set does not reflect reform in accounting systems for some countries and some years.

  8. The exception is Japan; given that there is no information on its GDP until 1970, we used the period of 1971–1997.

  9. Particularly, HE of Canada and USA and GDP of Germany and UK seem to be subject to several breaks.

  10. This is also done in Gerdtham and Lӧthgren (2000), Carrion-i-Silvestre (2005), and Jewell et al. (2003).

  11. We confirm that the differenced series are stationary.

  12. We find the null hypothesis of unit root is significantly rejected in Germany (HE and GDP) and Iceland (GDP) at the 5% or higher level. Even though the test with cumulative frequencies tends to capture the remaining nonlinearities as well as the overall smooth shifts, as we observe Table 5 of Enders and Lee (2012a), it results in lower power as we select a higher value of q. By minimizing SSR, we find that the selected q of 5 for most of the series. In such case, we estimate 8 more parameters than we do in the test with a single frequency. We observe that the I(1) property of the same series, which we confirm based on the tests with a single frequency, is supported in other literature based on different methodology (Gertham and Lӧthgren 2000; Clemente et al. 2004; Carrion-i-Silvestre 2005).

  13. The same number of maximum lags is recommended in Carrion-i-Silvestre (2005) based on the same data set.

  14. That is, the long-run equilibrium relationship is specified by:

    \( \ln {\text{HE}}_{t}^{i} = \mu_{1} + \mu_{2} t + \alpha \ln {\text{GDP}}_{t}^{i} + e_{t} .\)

  15. See Pesavento (2004) for more details.

  16. For example, see Gertham and Lӧthgren (2000) and Clemente et al. (2004). Based on the same point, Jewell et al. (2003) and Carrion-i-Silvestre (2005) examined the stationarity of HE and GDP using tests accommodating structural breaks.

  17. As done in Gregory and Hansen (1996a), we use the asymptotic critical value included in Table 1 of Gregory and Hansen (1996a) and listed the value used in Table 3.

  18. The selected optimal number of cumulative frequencies, q, is 5 in most countries. As we estimate more parameters in the testing regression, it seems inevitable to subject to the lower power of the tests. For more details, see the power properties examined in Table 5 of Banerjee et al. (2017).

  19. See also Fuinhas and Marques (2012).

  20. The existence of cointegration between the two series confirms that the estimated \( \delta \) is not zero and there exists a nonzero value \( \lambda \) which results in the linear relationship of the two non-stationary variables to be I(0).

  21. See also the discussion in Jewell et al. (2003).

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Authors and Affiliations

  1. Accounting, Economics and Finance, Tuskegee University, Tuskegee, AL, 36088, USA

    Hyejin Lee

  2. Department of Information Systems, Auburn University at Montgomery, Montgomery, AL, 36117, USA

    Dong-Yop Oh

  3. Model Risk Management Department, Fifth Third Bank, Cincinnati, OH, 45202, USA

    Ming Meng

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  1. Hyejin Lee
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  2. Dong-Yop Oh
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  3. Ming Meng
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Correspondence to Dong-Yop Oh.

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Lee, H., Oh, DY. & Meng, M. Stationarity and cointegration of health care expenditure and GDP: evidence from tests with smooth structural shifts. Empir Econ 57, 631–652 (2019). https://doi.org/10.1007/s00181-018-1561-1

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