Heterogeneous effect of coinsurance rate on healthcare expenditure: generalized finite mixtures and matching estimators

Abstract

The article proposes a combination of finite mixture models and matching estimators to account for heterogeneous and nonlinear effects of the coinsurance rate on healthcare expenditure. The analysis with panel data for adult Japanese consumers in 2008–2010 and for female consumers in 2000–2010 demonstrates the presence of subpopulations with high, medium and low healthcare expenditure, and subpopulation membership is explained by lifestyle variables. Generalized finite mixtures provide adequate fit compared to loglinear model. Conditional average treatment effect estimations reveal the existence of nonlinear effects of the coinsurance rate in the subpopulation with high expenditure.

Keywords:

• finite mixture model
• generalized linear model
• matching estimators
• health

JEL Classification:

• C440
• C610
• I130

Acknowledgements

The microdata of Japanese Panel Survey of Consumers and Japan Household Panel Survey were kindly provided by The Institute for Research on Household Economics (Tokyo) and The Keio University Panel Data Research Center (Tokyo), respectively.

The author is indebted to Noriyuki Sugiura, Kohei Komamura, Atsuhiro Yamada, Colin McKenzie, Hiroki Kawai (Keio University), Toshiaki Iizuka (University of Tokyo); Sergei Golovan, Ruben Enikolopov, Konstantin Styrin (New Economic School), Mark Pauly (University of Pennsylvania), Hitoshi Shigeoka (Simon Frauser University), Marcos Vera-Hernandez (University College London); Fuhito Kojima (Stanford University), participants of the 2014 conference of European Economic Association; 2013 Australasian meeting of the Econometric Society; 9th World Congress of the International Health Economics Association (2013); 4th and 5th Biennial Conferences of the American Society of Health Economists (2012 and 2014), 9th European Conference on Health Economics (2012), economic seminars at Hitotsubashi University, Institute of Economic Research (2012, 2011) and Keio University (2012, 2011), HSE/NES political economy seminar (2014), anonymous referees and the editor for helpful advice.

Notes

¹ Indeed, an illness episode, which encompasses various services offered over a period of time to provide the best cure for a particular medical problem, may be regarded as a natural unit for the analysis of healthcare demand (Hornbrook et al., 1985; Keeler and Rolph, 1988).

² Dependents in company-managed insurance commonly include housewives and nonworking children.

³ The predecessor of the current fee schedule is the schedule developed for office based physicians upon the introduction of health insurance for manual workers in 1927 (Campbell and Ikegami, 1998). The 1961 adoption of the universal health insurance retained the coexistence of the old fee schedule, favouring private practitioners and exploited by clinics and small hospitals, and the new schedule, supporting specialized care and used by hospitals (Ikegami, 1991; Campbell and Ikegami, 1998; National Institute of Population and Social Security Research, 2005). Additionally, an establishment of a separate health insurance for the elderly in 1982 led to an adoption of a special fee schedule for financing the treatment of this age cohort (Ikegami, 1991; National Institute of Population and Social Security Research, 2005). The three schedules are set by the MHLW, and the differences between the three schedules are minor (Ikegami, 1991). The old and new schedules were combined in 1994, and therefore, currently, a unified national fee schedule applies to all healthcare providers (Ikegami et al., 2011).

⁴ A point represented an average cost of daily drug dose in the first schedule of 1927 and became equivalent to 10 yen in 1961 (Campbell and Ikegami, 1998). It may be noted that till the end of the nineteenth century the Japanese doctors practising traditional medicine formally offered their services for free, asking reimbursement only for the cost of medicines used in the course of treatment (Campbell and Ikegami, 1998).

⁵ Neither health insurance society nor healthcare provider may negotiate fees besides the national schedule (Ikegami, 1991). Moreover, with the exception of obstetrics, preventive care, cosmetology and a number of additional types of treatment, balance billing, i.e. ‘charging the patient over and above the reimbursement from health insurance’ (Ikegami and Campbell, 2004), is prohibited.

⁶ The process resembles muddling through the items (Ikegami and Campbell, 1995), yet it proves an effective instrument for cost containment and volume control: first, the size of the aggregate increase in the costs of medical services and drugs is decided, and then the price of each item is altered individually (Ikegami, 1991). For example, in the 1980s–1990s, the schedule implemented bundling of fees to reduce the price of laboratory tests (Ikegami and Campbell, 1995); raised the fee for paediatric consultation since the number of patients decreased (Ikegami and Campbell, 1999). Moreover, some fees (e.g. for surgery) may be set below costs, so that such procedures could be provided mainly in public medical facilities, which receive subsidies (Arai and Ikegami, 1998). Overall, the purpose of the schedule is to restrict expensive services and favour low-cost items (Ikegami and Campbell, 1995). It may be noted that while lowering the general cost of drugs used to be sufficient for financing the increasing volume of medical services, the 2002 revision of unified fee schedule was the first to decrease the aggregate cost of medical services (Ikegami and Campbell, 2004; Ikegami, 2005, 2006). Accordingly, the fee for consequent consultations as well as the number of days with the basic charge in hospitals decreased (Nawata et al., 2006).

⁷ As for risky behaviours (smoking, drinking), index of psychological distress or weight, such questions are present only in the last one–three round(s) of questionnaire and therefore cannot be used for the analysis of pre-reform and post-reform data. Family size is excluded since it represents primarily adult family members in the sample of unmarried women without children. Therefore, family size is strongly correlated with household income.

⁸ The focus on outpatient care allows including dependents in non-national health insurance plans in a control group, as we may ignore simultaneous rise in the coinsurance rate for inpatient care of dependents.

⁹ As robustness check, we conduct our estimations with consumer out-of-pocket expenditure and obtain quantitatively similar results.

¹⁰ An alternative approach, based on Markov process assumptions about transition between components over time commonly applies to long panels and may fail to provide component-specific estimates (Collins and Lanza, 2010; Wouterse et al., 2013).

¹¹ Taking a weighted average of the fitted values for the dependent variable for each observation in all latent classes (Greene, 2005) does not enable contrasting behaviour of individuals from subpopulations.

¹² Alternative ways include Manning’s (1998) method, which is particularly easy to implement if heteroscedasticity is present across mutually exclusive groups; semi-parametric approaches and extensions of generalized linear models (Basu and Manning, 2009; Mullahy, 2009; Mihaylova et al., 2011).

¹³ The working status proved to be insignificant with our data and therefore is not included in the list of covariates.

¹⁴ In short, the quality of imputation is ensured by using covariates that explain most of variation of the imputed variable in the auxiliary sample (Japan Household Panel Survey); combining matching and regression to avoid imputation bias; examining the distance between matched observations, and analysing distributions of the imputed variable in the main and auxiliary samples. See Appendix 3 for details.

¹⁵ Our sample excludes people who had an illness that required hospitalization. Therefore, the analysis does not deal with coinsurance rates for inpatient care.

¹⁶ Following Andrews (1988), we use rectangular partitioning and the simple computation of the statistics. To account for annual effects we sum over individual clusters in matrix H, see Appendix 1 for details.

¹⁷ Indeed, in case of a two-component loglinear model $E{y}_1=2641.27$ (SD 712.06), while $E{y}_2=1031.66$ (SD 229.50). Generalized linear model with Weibull distribution family with two components produces very similar estimates: $E{y}_1^{\mathrm{g}\mathrm{l}\mathrm{m}}=2751.66$ (SD 703.84), $E{y}_2^{\mathrm{g}\mathrm{l}\mathrm{m}}=1223.73$ (SD 355.07). The three-component loglinear model yields $E{y}_1=3765.20$ (SD 1851.54), $E{y}_2=1686.24$ (SD 309.88), $E{y}_3=519.11$ (SD 253.40). Generalized linear model with a Weibull distribution family gives slightly lower mean values of the dependent variable for the first and second component, and higher mean value for the third component: $E{y}_1^{\mathrm{g}\mathrm{l}\mathrm{m}}=2847.45$ (SD 679.29), $E{y}_2^{\mathrm{g}\mathrm{l}\mathrm{m}}=1438.01$ (SD 415.63), $E{y}_3^{\mathrm{g}\mathrm{l}\mathrm{m}}=611.41$ (SD 284.28).

¹⁸ SEs are estimated using delta method.

¹⁹ Absence of children is positively related to the probability of belonging to the first component for all adult consumers.

²⁰ As was noted in Section III, owing to the system of medical benefits and medical expenditure deductions, the consumer price of healthcare may be lower than the nominal coinsurance rate, but various benefits and exemptions mostly apply to inpatient care, which is not studied in our analysis.

²¹ Arguably, health insurance premiums are not regarded as a potential component of healthcare expenditure. Indeed, the prevalence of zero reported healthcare expenditure among heads of household, who pay premiums and hence cannot have zero healthcare expenditure if premiums are considered a part of expenditure, is 47.0%. Moreover, Japan Household Panel Survey, which has a similar question on ‘health insurance expenditure’, introduces a special question on the amount of premiums.

²² The weight on the variable is 1000 larger than weights on other variables.

²³ We exploit regressions with two-parameter beta distribution or generalized linear models with log link and binomial distribution family and get similar results about the significance of coefficients for covariates. To increase sample size for imputations, we use pooled data of JHPS as coefficients for age and poor health in annual regressions explaining $q_j$ differ negligibly. To account for potential trade-off between healthcare services and drugs, covered and not covered by health insurance, we use two types of consumer price indexes: (1) for insurance-covered medical goods, services and drugs; and (2) for medical goods, not covered by health insurance. Both indexes proved insignificant and are not employed in the imputation.

²⁴ Since $\mathbf{x}$ and $\mathbf{z}$ have the same meaning and same units in both samples, we do not have to normalize them, as normalization might increase the bias.

²⁵ The matching and regressions results in 100% of exact matches, and mean distance between matched pairs in various years is less than 0.001 (min 0, max 0.23, SD <0.007).

²⁶ Age is calculated in full years in JPSC, which results in more than one match in JHPS.

²⁷ The season for respiratory diseases is late autumn–early winter.