Covid-19, out-of-pocket medical expenses and consumption

Jonathan E. Leightner (Hull College of Business, Augusta University, Augusta, Georgia, USA)

Journal of Financial Economic Policy

ISSN: 1757-6385

Article publication date: 22 February 2021

Issue publication date: 28 June 2021

485

Abstract

Purpose

Based upon estimates of the change in consumption due to a change in out-of-pocket-health expenses (dC/dOOPHE) for 43 countries, this paper aims to argue for a reevaluation of what constitutes OOPHE when determining health insurance especially in the wake of Covid-19.

Design/methodology/approach

Reiterative truncated projected least squares (RTPLS), a statistical technique designed to handle the omitted variables problem of regression analysis.

Findings

If budgets are binding than dC/dOOPHE should be 0; if OOPHE merely adds to current consumption than dC/dOOPHE should be 1. However, merely plotting consumption versus OOPHE for the 43 countries for which organization for economic cooperation and development has the required data clearly shows a dC/dOOPHE much greater than one. This paper’s estimates of dC/dOOPHE for 2000 to 2017 range from 15.6 for Switzerland (in 2016) to 225.2 for Columbia (in 2003).

Research limitations/implications

RTPLS cannot determine what part of the results are due to an increase in income causing both consumption and OOPHE to increase and what part is because of actual OOPHE far exceeding official OOPHE. However, the latter is involved.

Practical implications

As Covid-19 sickens millions while depriving millions of their normal means of generating income, what constitutes OOPHE should be expanded when determining health insurance. This paper’s results imply that even prior to Covid-19 health insurance covered much less than the optimal amount of actual OOPHE.

Originality/value

This is the first paper to use RTPLS to estimate dC/dOOPHE.

Keywords

Citation

Leightner, J.E. (2021), "Covid-19, out-of-pocket medical expenses and consumption", Journal of Financial Economic Policy, Vol. 13 No. 4, pp. 462-478. https://doi.org/10.1108/JFEP-04-2020-0087

Publisher

:

Emerald Publishing Limited

Copyright © 2021, Emerald Publishing Limited


Introduction

The Covid-19 pandemic that is currently sickening millions all around the world is forcing policymakers to reevaluate many standard policies. Two policies that need to be reevaluated is the percent of health expenses paid through health insurance and what constitutes out-of-pocket-health-expenses (OOPHE). Without health insurance, most families facing major health expenses would be forced into financial ruin. On the other extreme, if health insurance pays 100% of health expenses, then moral hazard becomes a problem – many people will take undo risks because any medical problems that result will be totally covered. Thus, the optimal amount of health insurance must lie somewhere between 0% and 100%. Surely Covid-19 is increasing the optimal percent by sickening millions while simultaneously depriving millions of their sources of income. Furthermore, if health insurance does not count some legitimate OOPHE when calculating insurance payments, then even an optimal insurance percent would result in too little payout. While the data needed to evaluate the effects of Covid-19 itself is not yet available, an examination of whether a pre-Covid-19 health insurance policy was optimal or not is a good starting point. One important piece of information needed is the relationship between consumption and OOPHE.

If budgets are binding then the change in consumption (C) due to a change in OOPHE should be zero; if OOPHE merely adds to current consumption then dC/dOOPHE should be one. However, merely plotting consumption versus OOPHE for the 43 countries for which organization for economic cooperation and development (OECD) has the required data clearly shows a dC/dOOPHE much greater than one.

This paper uses a statistical technique that is designed to handle the omitted variables problem with regression analysis to estimate a total derivative for dC/dOOPHE for these 43 countries. This technique produces a separate slope estimate for every observation where differences in these slope estimates are because of omitted variables. This paper finds dC/dOOPHE values for 2000 to 2017 that range from 15.6 for Switzerland (in 2016) to 225.2 for Columbia (in 2003). There are at least two explanations for these high values for dC/dOOPHE, namely, as income rises both consumption and OOPHE rise and official OOPHE is much lower than actual OOPHE. Official OOPHE would be much lower than actual OOPHE if actual OOPHE does not include medical expenditures outside of officially recognized medical institutions (e.g. visiting a chiropractor or using acupuncture or using herbal treatments), does not include the paying of medical bribes and/or does not include the replacing of an ill person’s home production with more expensive market provided services. To the extent that true OOPHE exceeds official OOPHE, the poverty increasing effects of OOPHE that other researchers have found is much worse than their numbers indicate and those who formulate health insurance policy need to seriously consider increasing the share of medical expenses placed on the insurance company. If health insurance covered too little pre-Covid-19, then Covid-19 is pushing the health insurance market even further from the optimal percent by sickening large numbers of people while devastating their sources of income.

Section 2 of this paper provides a literature survey. An important part of this literature survey discusses the difference between official OOPHE and actual OOPHE. Section 3 explains the statistical methods used. Section 4 presents the results, and Section 5 discusses these results. Section 6 concludes.

Literature survey

Out of love, many households will choose to sacrifice the future welfare of the entire family to provide health care that might save a sick family member. The future is sacrificed by going further into debt, selling productive assets or foregoing “investment in future productivity, for example, by curtailing children’s education.” These decisions can start a vicious cycle of increasing indebtedness and impoverishment (Van Damme et al., 2004) and sometimes nothing positive is gained due to the sick person remaining ill or dying. Thus, in addition to the productivity of the sick person falling due to illness, the productivity of all family members may fall due to lost or foregone resources (Gertler and Gruber, 2002; Kumar et al., 2015).

Kumar et al. (2015) find that every year approximately 7% to 8% of China’s and India’s population, respectively, fall in poverty due to out-of-pocket health expenditures (OOPHE). They also find that having a child under the age of five in the household and living in a rural area increases the chance of falling below the poverty line due to OOPHE. Poverty is likely to destroy the future of the children in these families. Garg and Karan (2009) found that in 1999 to 2000 OOPHE caused approximately 32.5 million people in India to fall below the poverty line. They point out that when OOPHE is deducted from income the overall poverty rate increased by 3.2% (in contrast to previous literature that showed a 2.2% increase). Analyzing data from 11 Asian countries, Van Doorslaer et al. (2006) find that taking into account OOPHE results in the incidence of absolute poverty in the countries analyzed being 14% higher than estimates that do not deduct OOPHE. They calculated that an additional 78 million people (2.7% of the population) were living on less than US$1 per day after OOPHE.

In Bangladesh, China, India, Nepal, and Vietnam, where more than 60% of health-care costs are paid out-of-pocket by households, our estimates of poverty were much higher than conventional figures, ranging from an additional 1.2% of the population in Vietnam to 3.8% in Bangladesh (see Wagstaff and Van Doorslaer, 2003, for more information on Vietnam).

Van Damme et al. (2004) report that the 26 out of the 72 Cambodian families surveyed that went into debt to pay medical expenses were still indebted a year later and were paying interest rates ranging from 2.5% to 15% per month. Some households were forced to sell their land. Van Damme et al. (2004) conclude that “in Cambodia, even relatively modest out‐of‐pocket health expenditure frequently causes indebtedness and can lead to poverty.” In 15 African countries, Leive and Xu (2008) found that coping with health expenditures through selling assets or borrowing money “ranged from 23% of households in Zambia to 68% in Burkina Faso” and families with the highest levels of income were less likely to resort to these methods.

OOPHE can have a devastating effect on households, destroying their current and future potential and driving them into a poverty trap from which they may never escape. However, what determines OOPHE? In Cambodia, VA Damme et al. (2004) find that households that used solely private health care providers “paid on average US$103; those who combined private and public providers paid US$32 and those who used only the public hospital US$8.” Does the perceived quality of private health care providers in Cambodia exceed the quality of public hospitals by a factor of more than 12.8 (US$103/US$8) especially for poor families who have to sell assets or go into debt to pay the OOPHE? [According to ‘out-of-pocket … older Americans’ (Crystal et al., 2000), OOPHE in the USA]

averaged 19.0% of income, for full-year Medicare beneficiaries alive during all of 1995 […]. higher-burden subgroups included those in poor health (28.5% of income), older than age 85 (22.4%), and with income in the lowest quintile (31.5%, despite Medicaid coverage for some).”

OOPHE goes up significantly as a person nears death (Zhou et al., 2003). Marshall et al. (2010) find that spending in the past year of life is estimated to be $11,618 on average, with the 90th percentile equal to $29,335, the 95th percentile $49,907 and the 99th equal to $94,310. For other studies that show how different socio-economic characteristics are related to OOPHE see Brinda et al. (2014) for Tanzania, Fahle et al. (2016) for the USA, Falkingham (2004) for Tajikistan, Gotsadze et al. (2005) for Georgia, Axelson et al. (2009) and Minh et al. (2013) for Vietnam, Chu et al. (2005) for Taiwan, Galbraith et al. (2005) for the USA and Xu et al. (2003) for 59 countries.

Different researchers have found contradictory results for the impact of insurance on OOPHE. Galárraga et al. (2010) found that Mexico’s public, voluntary insurance for the self-employed and unemployed (Seguro Popular) resulted in national catastrophic health expenditures falling by 54%. Finkelstein and McKnight (2008) found a 40% decline in OOPHE for the top quartile of the OOPHE distribution due to the introduction of Medicare in the USA in 1965, but Medicare did not reduce mortality. Nguyen (2011) found that people with voluntary health insurance annually make 70% more inpatient visits and 45% more outpatient visits than those without voluntary health insurance; “however, the effect of voluntary health insurance on out‐of‐pocket expenses on health care services is not statistically significant.” His results imply that the per-visit OOPHE of those with voluntary health insurance is lower, but that the increase in the number of visits produces approximately the same annual OOPHE. Leightner (2019) came to the same conclusion using data for 44 countries. The report out-of-pocket…older Americans” (Crystal et al., 2000) found that participation in an home maintenance organization is correlated with lower OOPHE, but that privately-purchased supplemental health insurance in the USA is positively correlated with higher OOPHE. You and Kobayashi (2011) find that in China, “certain types of insurance programs tend to increase out-of-pocket health expenditures” and that the share of OOPHE in total health expenditure “has increased in the past 25 years in China, from 20% in 1980 to 49% in 2006, with a peak of 59% in 2000.” Barros and Bertoldi (2008) point out that

the Brazilian public health system, free and universal, should limit out-of-pocket health expenses. However, Brazil was reported as one of the countries with the highest proportion of families experiencing catastrophic expenditure.

What “actually is” and what “should be” included in OOPHE? Some countries have medical insurance that have maximum OOPHE limits; however, the insurance companies only include deductibles and copayments when calculating OOPHE. They do not even count the insurance premiums in OOPHE. Nor do they count travel costs to and from medical facilities, nor non-prescription drugs, nor the cost of non-covered health care. In contrast, the US Government, for tax purposes, allows its citizens to include all the above as OOPHE. OECD, the source of my data, defines OOPHE as

Definition: Household out-of-pocket expenditure on health comprise cost-sharing, self-medication and other expenditure paid directly by private households, irrespective of whether the contact with the health care system [emphasis added] was established on referral or on the patient’s own initiative.

Context: The former relates to provisions of health insurance or third-party payers for beneficiaries to cover part of the medical cost via a fixed amount per service (co-payment) or a set share of the price tagged to services (co-insurance, also labeled in some countries 'ticket modérateur') or a fixed amount to be born before the third-party gets involved (deductible). Self-medication includes informal payments extracted by medical care providers [emphasis added] above the conventional fees, to over-the-counter prescriptions and to medical services not included in a third-party payer formulary or nomenclature of re-imbursable services (https://stats.oecd.org/glossary/detail.asp?ID=1967.

However, even OECD’s definition is vague because it does not spell out what is counted in the “health care system” and what makes a person a “medical care provider.”

Many people incur OOPHE, which are probably not counted in official OOPHE statistics because they cannot afford to go to the recognized “health care system.” For example, half of India’s babies are delivered at home without any official medical care (Mohanty and Srivastava, 2013), but delivering a baby at home still incurs costs that probably do not end up in official OOPHE estimates. Likewise, many people are attracted to acupuncture, chiropractic, homeopathy, hypnotherapy, medical herbalism, osteopathy, reflexology and aromatherapy medical treatments because of their expected lower costs, but these medical services might not be counted in official OOPHE statistics because they are not provided by the officially recognized “health care system.” Thomas et al. (2001) find that approximately 13.6% of England’s adult population used at least one of these therapies in the previous year. If “self-care using remedies purchased over the counter are included, the estimated proportion rises to 28.3% […] for use in the past 12 months and 46.6% […] for lifetime use.” In total, 90% of these visits were financed solely through out-of-pocket sources. Just the first six of these therapies result in an estimated out-of-pocket expenditure of £450m annually in England. They state that similar estimates for the USA and Australia also “indicate high levels of use and expenditure” for these types of services.

Nahin et al. (2016) estimate that 59 million Americans in 2012 purchased some kind of complementary medical product or service (which include visits to “complementary” health practitioners, natural product supplements and self-care products),

“resulting in total out-of-pocket expenditures of $30.2 billion[…].The mean per user out-of-pocket expenditure for complementary health approaches was $435 for persons with family incomes less than $25,000 and $590 for persons with family incomes of $100,000 or more.”

It is doubtful that all these expenses are included in OECD’s official estimates of OOPHE.

Furthermore, in many countries patients have to pay bribes to see doctors in a timely fashion and to receive the care they need at medical facilities. Chawla et al. (1998) for Poland find “that informal payments made by patients to physicians contribute as much as double of the physician’s salary, and thus, form an important source of earnings for physicians.” They believe that the same is true for “other transitional economies of Central and Eastern Europe.” The author of this paper believes that the same is true in many countries, both in the developing and developed world, especially where non-bribing patients face extremely long waits for medical care (Barber et al., 2004; for the case of Cambodia). It is doubtful that bribes are included in official OOPHE estimates.

Moreover, many medical problems require significant expenses all of which are probably not counted in official OOPHE statistics. For example, when a family member develops dementia, the family often spends a significant amount of money insuring that the dementia member does not wander off and get lost or burn down the house by forgetting that they were cooking. Indeed many people with severe dementia require that someone watch them continuously because the family does not want to lock the member with dementia away where they cannot hurt themselves and others (Langa et al., 2004). Families of those who develop physical disabilities often have to spend significant amounts of money on home modifications. Furthermore, and importantly, if a productive member of a family becomes sufficiently ill, then what that member used to produce usually needs to be replaced. For example, if the person who used to cook for a family becomes too ill to cook, then the cost of feeding the family usually goes up. Likewise, if the family member that took care of home maintenance becomes ill, then the family is likely to spend more on home maintenance than before. These types of expenses would not be captured in official OOPHE statistics. The above literature is a small part of a broader literature that deals with insurance in general. This broader literature includes Sommervoll and Wood (2011), Gehrig and Iannino (2018) and Kaushal and Ghosh (2018).

Methods

To correctly use traditional econometric methods to estimate the change in per capita consumption dC/dOOPHE, a researcher would need to create a structural model that correctly modeled all the ways that per capita consumption and per capita OOPHE are connected, estimate every equation in that model and then solve that model for the desired reduced form equation. For example, an equation would need to be developed and estimated that captured a given population’s preference for health care versus other consumption goods. Of course, that relationship will depend upon the health condition of that population, on the short-run and long-run consequences of not addressing current health problems, on the health problems that private and public insurance covers, on the percent of health costs that insurance covers, on the costs and availabilities of different medical alternates, on the perceived efficacy of different medical alternates, on the relative costs of health and non-health consumption goods, etc.

If the researcher would try to directly estimate dC/dOOPHE without going through this process, then his or her estimates would be biased from simultaneous equation bias and omitted variable bias. Using instrumental variables is the standard approach to the omitted variable’s problem. However, to correctly use instrumental variables, the researcher must find instruments that are highly correlated to the omitted variable and that are not related to the dependent variable except through their relationship with the omitted variables. If such variables are found, which is highly unlikely, the researcher must correctly model how the omitted variable affects the dependent variable and how the instrument is related to the omitted variable (Leightner and Inoue, 2007). All of these conditions are impossible to meet for a subject as complex as the relationship between per capita consumption and OOPHE.

To avoid omitted variable bias, this paper uses a statistical technique that uses the relative vertical position of observations to capture the influence of omitted variables (and thereby eliminates simultaneous equation bias). This technique produces a separate slope estimate for every observation where differences in these slope estimates are because of omitted variables. The major advantage of this technique is that the researcher does not need to construct and justify a correct structural model, get all the data required by that model and then solve the model after all the equations are estimated. A major disadvantage of this technique is that it cannot tell the researcher the mechanisms via which the independent variable is affecting the dependent variable. Thus, this technique is not a substitute for traditional econometric methods and theory; it is a compliment to them.

If a researcher estimates equation (1) while ignoring equation (2), the resulting estimate of β1 is a constant when in truth β1 varies with qi (The αs and βs are coefficients to be estimated, Y is the dependent variable, X is the explanatory variable and u is random error). This constitutes an “omitted variable” problem where “qt” represents the combined influence of all omitted variables plus any random variation in β1 itself.

(1) Yt=α0+β1Xt+u
(2) β1=α1+α2qt

One convenient way to model the omitted variable problem is to combine equations (1) and (2) to produce equation (3).

(3) Yt=α0+α1Xt+α2Xtqt+ut.

Equation (7) can be derived from equation (3) as shown below (Leightner, 2015 and Leightner and Inoue, 2012).

(4) (dYt/dXt)True=α1+α2qt        Derivative of (3)
(5) Yt/Xt=α0/Xt+α1+α2qt+ut/Xt   (3)dividedbyX
(6) α1+α2qt=Yt/Xtα0/Xtut/Xt    (5)rearranged
(7) (dYt/dXt)True=Yt/Xtα0/Xtut/Xt   Fromequations (4)and(6)

If an estimate for α0 could be found, then it could be used to calculate a separate slope estimate for each observation using equation (8). The error due to such a procedure is shown in equation (9). The ut/Xt term in equation (9) should be extremely small because random error, ut, is usually tiny relative to the size of Xt, making ut/Xt even smaller. This implies that the accuracy of calculating a separate slope estimate for each observation using equation (8) depends primarily upon the accuracy of the α0 estimate.

(8) (dYt/dXt)=Yt/Xtα0/Xt
(9) (dYt/dXt)True (dYt/dXt)=(α0α0)/Xtut/XtFrom(7)and(8)

Reiterative truncated projected least squares (RTPLS) produces separate slope estimates for layers of the data by peeling the data down layer by layer and then peeling the data up after which equation (10) is used with the resulting layer slopes ((dYt/dXt) ^) to estimate α0. In essence, RTPLS uses the relative vertical position of observations as a measure of the combined influence of all omitted variables – for any given value of X, the reason that some observations have higher (or lower) values for Y is because of the influence of omitted variables. The open access article Leightner and Inoue (2012) explains the math that underlies RTPLS.

(10) (dYt/dXt)Yt/Xt=α0/Xt   (8)rearranged

The estimate of α0 found by estimating equation (10) along with data for Yt and Xt are plugged into equation (8) to calculate a separate slope estimate for every observation.

Leightner (2015) shows that when the omitted variable problem is ignored by estimating equation (1) using ordinary least squares (OLS), the resulting estimate for β1 is approximately α1+ α2E[qt], which leaves an “error” for the t = ith observation of approximately α2Xi(qi – E[qi]) + ui. Using RTPLS is better than ignoring the omitted variables problem if |(α0^ – α0)/Xiui/Xi| is less than |α2{qi – E[qi]}|.

Leightner (2015) and Leightner and Inoue (2012) present simulation tests for RTPLS, which show that RTPLS noticeably out performs using OLS while ignoring the omitted variables problem except for the case where the omitted variable makes only a 10% difference to the slope and random error is 10%. When the importance of the omitted variable was 100 times as big as random error, using OLS while ignoring omitted variables produced approximately 35 times the error of RTPLS. When the importance of the omitted variable was 10 times as big as random error, then using OLS while ignoring omitted variables produced approximately 3.8 times the error of RTPLS. Academic journals that have published applications of RTPLS include International Journal of Contemporary Mathematical Sciences, European Journal of Operations Research, Economics Bulletin, Journal of Central Banking Theory and Practice, International Journal of Financial Research, Economies, China Economic Policy Review, Applied Economic Letters, Frontiers of Economics in China, China and World Economy, Pacific Economic Review, The Japanese Economy: Translations and Studies, Journal of Productivity Analysis, Economy, International Economics and Finance Journal, Advances in Decision Sciences, International Journal of Economic Issues, Global Economy Journal and Contemporary Social Science.

Leightner (2015) explains how the central limit theorem can be used to create confidence intervals for RTPLS estimates as shown in equation (11):

(11) confidence interval=mean±(s/n)tn1, α/2

In equation (11), s is the standard deviation, n is the number of observations and tn-1, α/2 is taken off the standard t table for the desired level of confidence. Leightner (2015) uses a given estimate and the 2 estimates before and after it and a 99% confidence level, to create a moving confidence interval (much like a moving average) for a given set of RTPLS estimates. This 99% confidence interval can be interpreted as meaning that there is only a 1% chance that the next RTPLS estimate will lie outside of this range if the omitted variables maintain the same amount of variability that they recently have. All of the dC/dOOPHE estimates in this paper were statistically different from zero at a 99% confidence level (except for the first two and last two observations for each country because the above process does not calculate confidence intervals for them).

RTPLS generates reduced form estimates that include all the ways that X and Y are correlated. Thus, even when many variables interact via a system of equations, a researcher using RTPLS does not have to discover and justify that system of equations. In contrast, traditional regression analysis theoretically must include all relevant variables in the estimation and the resulting slope estimate for dY/dX is for the effects of just X – holding all other variables constant. RTPLS’s reduced form estimates are not substitutes for traditional regression analysis’ partial derivative estimates. Instead, RTPLS and traditional regression estimates are compliments, which capture different types of information. RTPLS has the disadvantage of not being able to tell the researcher the mechanism by which X affects Y. On the other hand, RTPLS has the significant advantage of not having to model and find data for all the forces that can affect Y to estimate dY/dX. Both RTPLS and traditional regression techniques find “correlations.” It is impossible for either one of them to prove “causation.”

Results

This paper used the maximum amount of data available on the OECD website. To get consumption per capita, total consumption was divided by the population. The population data was downloaded from the UN data website because OECD stopped updating its population data after 2014. To save space, Table 1 provides the OOPHE data and Table 2 the dC/dOOPHE estimates for 2000 and afterward. However, the actual data used started in 1970 for Denmark, Finland, France, Germany, Italy, Korea and the USA; 1971 for Australia; 1979 for Turkey; 1980 for New Zealand and the UK; 1983 for Ireland; 1985 for Iceland; 1988 for Canada; 1990 for the Czech Republic, Norway and Poland; 1991 for Hungary and Spain; in 1995 for Israel, Japan, Luxembourg and Switzerland; 1997 for Slovakia; 1998 for The Netherlands; 1999 for Estonia and Mexico; 2003 for Belgium and Slovenia; 2008 for Greece; 2012 for Costa Rica; and in 2000 for the remaining countries listed in the tables. However, there were missing data for France in 1971 to 1974, 1976 to 1979, 1981 to 1984 and 1986 to 1989, for Germany in 1991, for New Zealand in 1981, 1983 and 2003 and for the UK in 1981 to 1989. The right-hand side of Tables 1 and 2 show when the data ended for each country. There was a total of 1097 observations.

Table 1 shows that OOPHE (for 2000–2017) ranged from US$35 per person in Columbia in 2003 to US$2313 per person in 2016 in Switzerland. Table 1 also shows that between 2000 and 2017 OOPHE doubled for many countries and even quadrupled for some countries. The two exceptions to a noticeable rise in OOPHE are Greece where official OOPHE declined from 2008 to 2012, during the height of her financial crisis, and South Africa where OOPHE has been relatively stable over time.

All the data is depicted in Figure 1, which clearly shows a positive correlation between per capita OOPHE and per capita consumption where the slope is much greater than one (note that the y-axis is measured in thousands of US dollars and the x-axis in just US dollars). Recall that if consumers are at a binding constraint (due to a budget or debt limits), then dC/dOOPHE should equal zero (as consumption cannot increase due to the binding constraint). If however, OOPHE just adds additional consumption (without causing the consumption of other goods to fall), then dC/dOOPHE should equal one (as OOPHE is included in consumption). The fact that dC/dOOPHE is much greater than one is unexpected and important. The strands of the data in Figure 1 that emanate from the origin (many of which are associated with a specific country) imply that the variation in this data is not solely due to random error. For example, the bottom, right-hand side strand is for Switzerland.

The RTPLS estimates for dC/dOOPHE are given in Table 2.

Switzerland, which had the highest OOPHE in 2016, had the lowest dC/dOOPHE in that year of US$15.6 per capita. However, US$15.6 per capita is noticeably greater than the expected value of one or less. Columbia, with the lowest OOPHE in 2003, had the highest dC/dOOPHE in that year of US$225.2 per capita. However, for many countries, the magnitude of the fall in dC/dOOPHE was much less than the magnitude of the rise in OOPHE. Israel, which experienced an overall rise in OOPHE from 2000 to 2017 even had an overall rise in dC/dOOPHE.

Discussion

There are at least two explanations for why the dC/dOOPHE estimates are large. First, if an increase in income is correlated with an increase in both consumption and OOPHE, then the RTPLS estimates of dC/dOOPHE (which are total derivatives, not partial derivatives) would capture that common correlation. Second, actual OOPHE probably far exceeds reported OOPHE due to spending on non-officially recognized medical treatments such as acupuncture, chiropractic and homeopathy, paying of medical bribes, spending on home modifications due to medical conditions and replacing the household production activities of ill members with more expensive alternates. Both explanations are probably involved in my results; however, to the extent that the second explanation is true, the induced poverty from OOPHE that Kumar et al. (2015), Garg and Karan (2009) and Van Doorslaer et al. (2006) found is worse than their results show.

Furthermore, a rise in income causing both consumption and OOPHE to rise cannot explain why the dC/dOOPHE estimates are changing over time (at a 99% confidence level) for the 31 countries marked by an “*” in Table 2. If only a rise in income was involved then dC/dOOPHE should be constant over time. For these countries, there must have been a change in preference between OOPHE and other consumption goods, a change in health costs, a change in what health insurance covers, a change in the relative price of health care and other consumption items, a change in the health condition of the population and/or some other related force.

RTPLS cannot determine how much of this paper’s results are due to a rise in income causing both consumption and OOPHE to increase versus how much is due to actual OOPHE far exceeding official OOPHE. What is certain is that a rise in income cannot explain all of this paper’s results because a rise in income cannot explain why dC/dOOPHE is changing over time, insurance companies do not consider health expenses outside of official health channels, insurance companies do not consider medical bribes, insurance companies do not consider all home modifications due to medical conditions, insurance companies do not consider the cost of replacing the home production of sick family members with more expensive market alternates. Because of all the expenses associated with medical problems that health insurance does not consider, it is highly probably that even prior to Covid-19 health insurance was covering far less than the optimal percent of health expenses.

Conclusion

Although this paper was unable to determine the optimal percent of health expenses that insurance should cover, this paper’s results imply that prior to Covid-19 health insurance was covering less than the optimal percent (this sub-optimality was partially because health insurance does not consider many OOPHE). Covid-19 has sickened millions while simultaneously depriving millions of their normal income sources. Thus, Covid-19 has increased the optimal percent that health insurance should cover. Moreover, this paper (and all other papers that look at health expenditures on a macro level) conceals the catastrophic impact of medical bills on the households hardest hit by those bills (Van Damme et al., 2004). In other words, the dC/dOOPHE estimates of this paper are for what happens on average in a given country in a given year – these estimates do not show the destruction and heartache that accompanies a family member becoming ill and the rest of the family sacrificing their future in the hopes of some cure, which often does not come.

Clearly, more research needs to be conducted on the optimal percent of actual health expenses that health insurance should cover and on what constitutes legitimate OOPHE, especially in the context of a major pandemic such as Covid-19.

Figures

Per capita: out of pocket medical expenses verse consumption

Figure 1.

Per capita: out of pocket medical expenses verse consumption

Per capita out-of-pocket medical expenses in US$

Country 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Australia 452 464 483 487 528 558 598 607 630 679 713 727 759 824 841 836
Austria 482 509 545 579 633 647 674 706 733 755 799 835 885 945 966 981 998 1,396
Belgium 568 533 525 571 611 632 670 696 729 742 783 791 755 739
Brazil 278 300 302 284 302 319 332 342 331 349 335 344 356 361 386 397
Canada 402 415 436 444 470 504 554 570 587 616 649 625 629 647 660 670 690 712
China 78 86 96 105 111 121 128 128 138 155 157 177 199 219 231 247
Columbia 48 51 44 35 61 82 102 122 145 136 129 120 122 121 148 157
Costa Rica 272 263 288 277 272
Czech Rep. 94 110 113 132 142 155 172 214 286 303 293 302 312 323 348 328 373
Denmark 357 376 393 399 441 457 497 529 554 589 640 656 650 656 671 684 696
Estonia 99 95 113 131 158 168 240 246 270 273 300 308 326 374 401 423 451 475
Finland 424 439 462 435 467 486 543 585 632 651 687 705 706 743 745 809 838
France 182 196 205 210 215 230 309 327 365 394 409 429 433 452 461
Germany 327 344 372 396 443 463 505 528 549 579 612 635 652 644 651 672 677 690
Greece 1,140 843 758 735 677 740 782 791 777
Hungary 220 260 285 331 326 352 357 361 387 393 444 486 506 504 513 538 584
Iceland 517 546 573 553 588 587 573 570 594 618 615 621 638 663 681 699 710 746
India 59 68 69 71 75 81 85 90 91 94 95 94 103
Indonesia 42 45 50 60 60 93 99 107 103 108 161 165 167 167 173 192
Ireland 216 222 246 334 341 419 463 422 478 554 628 655 681 700 700 693 684
Israel 500 547 502 483 509 535 456 506 485 493 482 508 528 546 559 600 626
Italy 542 532 545 542 551 543 583 597 647 640 645 707 704 704 720 762 792 834
Japan 305 319 336 372 386 386 424 422 435 456 467 498 521 534 546 573
Korea 316 367 366 399 418 459 498 555 617 606 656 682 722 743 785 844 895 993
Latvia 208 255 276 294 309 338 322 370 408 403 402 378 436 471 509 589 712
Lithuania 142 157 165 180 236 269 307 312 367 358 378 419 493 537 550 594 644 648
Luxembourg 486 510 572 578 627 662 735 568 602 639 661 626 644 658 722 715 724 726
Mexico 253 283 303 358 371 399 415 432 412 421 416 403 429 429 424 429 412
The Netherlands 211 223 228 227 237 367 342 351 468 437 455 482 529 619 644 598 600 605
New Zealand 247 290 296 280 299 332 280 360 365 358 377 391 420 451 471 494 500
Norway 511 514 575 590 629 665 704 723 769 766 777 830 849 873 885 882 897 930
Poland 176 183 189 202 231 224 238 259 285 309 321 341 359 373 370 392 409 442
Portugal 395 402 393 431 460 500 566 598 643 643 659 671 697 684 718 735 772 787
Russia 111 127 148 170 177 194 238 268 336 408 387 397 425 463 485 504 528
Slovakia 65 72 81 94 206 259 344 416 347 411 444 452 473 490 360 374 387
Slovenia 213 220 248 247 282 294 301 302 301 315 326 341 334 333 333
South Africa 85 84 80 80 80 82 82 80 78 76 75 77 79 81 83 84
Spain 357 387 408 426 446 467 508 537 583 567 598 615 663 705 741 755 776
Sweden 314 408 431 436 464 481 520 555 589 600 598 703 754 788 804 816 815 834
Switzerland 1,182 1,232 1,251 1,282 1,351 1,331 1,381 1,482 1,551 1,613 1,653 1,726 1,843 1,928 2,080 2,201 2,313
Turkey 95 91 108 141 166 186 161 123 147 145 146 166 185 174 180
UK 182 199 215 237 231 231 259 274 263 278 298 305 305 568 583 608 630
USA 705 724 762 812 849 893 916 963 971 957 969 995 1,014 1,028 1,036 1,057 1,090 1,122

Per capita: the change in consumption in US$ due to a one dollar increase in out-of-pocket medical expenses

Country 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Australia* 42.9 42.9 43.0 44.2 42.3 41.2 40.7 41.6 39.3 38.6 36.8 37.2 35.9 35.9 35.7 36.4
Austria* 37.7 36.1 34.8 33.9 32.2 32.6 32.9 32.0 32.0 31.7 30.6 30.8 30.2 29.2 28.6 28.5 28.8 21.2
Belgium 32.6 35.5 36.9 35.6 34.3 34.8 33.0 33.1 32.4 32.7 31.9 32.0 33.8 35.7
Brazil* 31.1 29.2 28.9 31.0 29.7 29.2 29.1 29.7 32.0 31.1 33.8 33.9 34.0 34.6 33.3 32.0
Canada* 45.7 45.7 45.0 45.7 44.3 43.5 41.4 41.8 41.1 39.8 38.5 40.6 40.9 41.5 41.8 41.3 41.0 40.9
China* 53.7 49.5 45.9 43.2 41.9 40.0 39.4 41.7 40.1 37.5 38.7 36.8 34.7 33.3 33.5 33.5
Columbia* 152.6 147.6 176.6 225.2 134.1 103.2 87.2 77.2 66.3 71.5 77.0 86.0 87.8 92.5 78.9 79.4
Costa Rica 44.2 46.7 43.9 46.2 48.0
Czech Rep.* 115.4 104.2 104.5 94.0 90.4 84.7 80.4 68.4 55.2 52.8 55.1 55.5 54.2 54.7 52.1 55.9 51.2
Denmark* 44.5 42.8 42.6 42.3 40.9 40.9 40.2 39.3 39.3 36.9 35.4 35.7 36.4 37.2 36.7 36.8 37.2
Estonia* 79.5 87.8 81.0 75.3 67.8 69.6 54.7 58.3 54.8 49.4 46.0 48.3 48.2 44.3 42.4 40.9 40.3 40.0
Finland 35.6 35.3 34.8 38.2 37.6 37.1 35.4 34.8 34.4 33.3 32.6 33.5 33.9 32.7 33.0 30.9 30.7
France* 92.3 89.8 88.7 86.0 86.2 84.2 65.9 64.9 60.1 55.8 55.3 54.3 53.9 53.8 53.2
Germany* 55.1 54.5 51.2 49.6 46.0 45.0 43.2 42.4 42.5 40.7 39.6 40.6 40.5 42.0 42.4 41.1 42.1 43.1
Greece 20.1 27.1 28.6 27.8 29.2 28.3 27.2 26.6 27.3
Hungary* 41.5 37.6 37.0 34.1 35.3 33.8 34.5 35.7 35.2 34.6 31.1 29.9 29.4 30.2 29.7 28.8 27.1
Iceland 38.7 36.3 34.7 37.4 37.8 40.8 42.5 44.0 41.3 37.9 36.6 37.5 38.5 38.2 38.3 37.7 39.4 40.5
India 70.4 62.4 61.5 61.3 58.4 56.2 55.5 54.8 55.2 55.1 56.6 59.9 55.7
Indonesia* 136.7 132.2 125.4 109.2 111.7 73.7 70.6 69.0 72.3 69.9 46.1 46.5 48.3 50.6 50.5 47.0
Ireland* 78.4 79.3 74.8 56.4 57.5 48.6 47.9 56.4 50.1 40.2 36.7 35.5 34.5 34.5 35.1 36.7 38.5
Israel* 31.3 29.2 32.6 32.2 32.2 30.3 36.7 35.6 37.6 36.3 38.9 38.9 38.2 39.1 39.7 37.8 38.4
Italy 35.0 36.2 35.8 36.8 36.7 38.0 37.6 38.3 36.7 36.8 37.1 35.2 35.3 35.1 34.3 33.0 33.1 32.9
Japan* 56.1 55.4 54.3 50.1 50.1 52.0 49.4 51.4 51.1 48.1 48.4 46.5 46.3 47.3 45.8 43.6
Korea* 39.0 35.6 38.5 35.1 34.2 32.9 32.3 30.6 28.2 28.0 26.9 26.7 25.9 25.2 24.2 23.3 22.4 20.9
Latvia 37.6 32.8 32.5 32.5 33.4 33.0 39.7 36.5 34.1 32.0 34.4 39.1 35.6 34.6 33.3 29.4 25.2
Lithuania* 58.4 57.3 58.0 58.6 47.7 45.1 43.4 47.4 44.1 42.3 41.1 40.1 36.2 35.7 36.5 34.9 34.2 36.3
Luxembourg 47.7 46.9 43.8 44.3 42.1 40.7 38.9 51.4 50.7 47.0 44.6 49.2 48.6 48.7 45.6 46.3 46.0 47.1
Mexico* 41.1 37.3 35.2 30.2 29.7 28.2 28.5 28.2 30.6 28.9 30.2 33.0 32.0 33.1 34.3 34.0 36.2
The Netherlands* 88.5 85.7 87.0 86.4 85.3 57.0 63.8 65.0 50.5 52.2 50.4 49.2 45.3 40.1 38.3 41.9 42.3 44.2
New Zealand 60.8 52.6 53.9 60.5 58.4 56.4 68.4 54.7 55.6 57.4 57.3 56.2 55.6 53.0 50.8 50.9 52.1
Norway* 35.0 35.6 33.2 33.4 33.2 33.1 33.6 33.9 33.1 32.8 33.5 32.1 32.4 32.6 32.2 31.3 30.8 31.1
Poland* 54.3 54.1 55.7 53.1 49.0 51.2 50.7 49.4 49.0 47.0 48.1 48.3 47.7 46.9 48.2 46.6 46.0 45.6
Portugal* 36.6 36.7 38.7 36.2 35.0 34.1 32.4 31.8 31.1 30.2 30.8 29.7 28.5 29.9 29.4 29.4 29.1 29.6
Russia* 56.1 52.9 48.8 46.1 47.6 47.7 45.1 43.6 40.4 35.2 37.0 37.5 37.4 35.9 34.3 30.7 28.9
Slovakia* 138.2 135.2 127.2 113.0 54.9 46.5 38.5 34.5 46.1 40.0 38.3 38.4 37.7 37.3 51.7 50.1 50.0
Slovenia 67.0 68.1 62.2 64.3 59.2 60.4 58.6 60.0 62.1 60.3 58.5 56.8 58.0 60.8 65.1
South Africa* 92.0 95.1 98.8 100.8 106.2 109.8 114.6 122.1 126.9 127.9 131.6 131.2 132.4 132.2 129.9 127.2
Spain* 43.4 41.9 41.4 40.0 39.9 39.7 39.8 39.3 36.9 36.4 34.8 34.2 32.1 30.5 30.0 30.0 30.3
Sweden* 51.3 39.4 38.5 38.8 38.1 37.2 36.6 36.5 35.5 34.9 36.0 31.9 30.5 29.8 29.4 29.4 29.8 30.4
Switzerland* 19.4 19.1 19.2 18.8 18.3 19.0 19.5 19.4 19.3 18.7 18.5 18.4 17.8 17.5 16.6 16.2 15.6
Turkey 96.1 96.2 81.2 64.5 59.2 55.9 70.0 97.9 85.9 85.1 93.7 91.3 84.4 95.1 97.0
UK* 108.8 103.6 100.5 93.7 100.4 102.0 94.9 91.5 98.1 89.4 85.2 84.6 87.4 49.0 48.9 47.2 46.8
USA* 37.2 37.3 36.3 35.4 35.5 35.5 36.1 35.5 35.7 35.5 35.9 36.2 36.3 36.4 37.4 37.8 37.7 37.9

Note: *= between 2000 and 2017 there was a statistically significant change (at a 99% confidence level) in these estimates for the indicated country

References

Axelson, H., Bales, S., Minh, P.D., Ekman, B. and Gerdtham, U.-G. (2009), “Health financing for the poor produces promising short-term effects on utilization and out-of-pocket expenditure: evidence from Vietnam”, International Journal for Equity in Health, Vol. 8 No. 1, Article No. 20, doi: 10.1186/1475-9276-8-20.

Barber, S., Bonnet, F. and Bekedam, H. (2004), “Formalizing under-the-table payments to control out-of-pocket hospital expenditures in Cambodia”, Health Policy and Planning, Vol. 19 No. 4, pp. 199-208, doi: 10.1093/heapol/czh025.

Barros, A.J. and Bertoldi, A.D. (2008), “Out-of-pocket health expenditure in a population covered by the family health program in Brazil”, International Journal of Epidemiology, Vol. 37 No. 4, pp. 758-765, doi: 10.1093/ije/dyn063.

Brinda, E.M., Andrés, R.A. and Enemark, U. (2014), “Correlates of out-of-pocket and catastrophic health expenditures in Tanzania: results from a national household survey”, BMC International Health and Human Rights, Vol. 14 No. 1, doi: 10.1186/1472-698X-14-5.

Chawla, M., Berman, P. and Kawiorska, D. (1998), “Financing health services in Poland: new evidence on private expenditures”, Health Economics, Vol. 7 No. 4, doi: 10.1002/(SICI)1099-1050(199806)7:4<337::AID-HEC340>3.0.CO;2-Z.

Chu, T.B., Liu, T.C., Chen, C.S., Tsai, Y.W. and Chiu, W.T. (2005), “Household out-of-pocket medical expenditures and national health insurance in Taiwan: income and regional inequality”, BMC Health Services Research, Vol. 5 No. 1, doi: 10.1186/1472-6963-5-60.

Crystal, S., Johnson, R., Harman, J., Sambamoorthi, U. and Kumar, R. (2000), “Out-of-pocket health care costs among older Americans”, The Journals of Gerontology: Series B, Vol. 55 No. 1, pp. S51-S62, doi: 10.1093/geronb/55.1.S51.

Fahle, S., McGarry, K. and Skinner, J. (2016), “Out-of-pocket medical expenditures in the United States: evidence from the health and retirement study”, Fiscal Studies, Vol. 37 Nos 3/4, pp. 785-819, doi: 10.1111/j.1475-5890.2016.12126.

Falkingham, J. (2004), “Poverty, out-of-pocket payments and access to health care: evidence from Tajikistan”, Social Science and Medicine, Vol. 58 No. 2, pp. 247-258, doi: 10.1016/S0277-9536(03)00008-X.

Finkelstein, A. and McKnight, R. (2008), “What did medicare do? The initial impact of medicare on mortality and out of pocket medical spending”, Journal of Public Economics, Vol. 92 No. 7, pp. 1644-1668, doi: 10.1016/j.jpubeco.2007.10.005.

Galárraga, O., Sosa-Rubí, S.G., Salinas-Rodríguez, A. and Sesma-Vázquez, S. (2010), “Health insurance for the poor: impact on catastrophic and out-of-pocket health expenditures in Mexico”, The European Journal of Health Economics, Vol. 11 No. 5, pp. 437-447.

Galbraith, A.A., Wong, S.T., Kim, S.E. and Newacheck, P.W. (2005), “Out‐of‐pocket financial burden for low‐income families with children: socioeconomic disparities and effects of insurance”, Health Services Research, Vol. 40 No. 6p1, doi: 10.1111/j.1475-6773.2005.00421.x.

Garg, C.C. and Karan, A.K. (2009), “Reducing out-of-pocket expenditures to reduce poverty: a disaggregated analysis at rural-urban and state level in India”, Health Policy and Planning, Vol. 24 No. 2, pp. 116-128, doi: 10.1093/heapol/czn046.

Gehrig, T. and Iannino, M.C. (2018), “Capital regulation and systemic risk in the insurance sector”, Journal of Financial Economic Policy, Vol. 10 No. 2, pp. 237-263, doi: 10.1108/JFEP-11-2017-0105.

Gertler, P. and Gruber, J. (2002), “Insuring consumption against illness”, American Economic Review, Vol. 92 No. 1, pp. 51-70, doi: 10.1257/000282802760015603.

Gotsadze, G., Bennett, S., Ranson, K. and Gzirishvili, D. (2005), “Health care-seeking behaviour and out-of-pocket payments in Tbilisi, Georgia”, Health Policy and Planning, Vol. 20 No. 4, pp. 232-242, doi: 10.1093/heapol/czi029.

Kaushal, S. and Ghosh, A. (2018), “Banking, insurance and economic growth in India: an empirical analysis of relationship from regulated to liberalized era”, Journal of Financial Economic Policy, Vol. 10 No. 1, pp. 17-37, doi: 10.1108/JFEP-03-2017-0022.

Kumar, K., Singh, A., Kumar, S., Ram, F., Singh, A., Ram, U., Negin, J. and Kowal, P.R. (2015), “Socio-economic differentials in impoverishment effects of out-of-pocket health expenditure in China and India: evidence from WHO SAGE”, Plos One, Vol. 10 No. 9, doi: 10.1371/journal.pone.0138499.

Langa, K.M., Larson, E.B., Wallace, R.B., Fendrick, A.M., Foster, N.L., Kabeto, M.U., Weir, D.R., Willis, R.J. and Herzog, A.R. (2004), “Out-of-pocket health care expenditures among older americans with dementia”, Alzheimer Disease and Associated Disorders, Vol. 18 No. 2, pp. 90-98.

Leightner, J.E. (2015), The Limits of Fiscal, Monetary, and Trade Policies: International Comparisons and Solutions, World Scientific, Singapore.

Leightner, J.E. (2019), “Does health insurance decrease out-of-pocket health expenses?”, Economics Bulletin, Vol. 39 No. 4, pp. 2589-2594.

Leightner, J.E. and Inoue, T. (2007), “Tackling the omitted variables problem without the strong assumptions of proxies”, European Journal of Operational Research, Vol. 178 No. 3, pp. 819-840.

Leightner, J.E. and Inoue, T. (2012), “Solving the omitted variables problem of regression analysis using the relative vertical position of observations”, Advances in Decision Sciences, Vol. 2012, available at: http://dx.doi.org/10.1155/2012/728980/.

Leive, A. and Xu, K. (2008), “Coping with out-of-pocket health payments: empirical evidence from 15 African countries”, Bulletin of the World Health Organization, Vol. 86 No. 11.

Marshall, S., McGarry, K.M. and Skinner, J.S. (2010), “The risk of out-of-pocket health care expenditure at end of life”, NBER Working Paper No. 16170.

Minh, H.V., Phuong, N.T.K., Saksena, P., James, C.D. and Xu, K. (2013), “Financial burden of household out-of pocket health expenditure in Viet Nam: findings from the national living standard survey 2002–2010”, Social Science and Medicine, Vol. 96, pp. 258-263, doi: 10.1016/j.socscimed.2012.11.028.

Mohanty, S.K. and Srivastava, A. (2013), “Out-of-pocket expenditure on institutional delivery in India”, Health Policy and Planning, Vol. 28 No. 3, pp. 247-262, doi: 10.1093/heapol/czs057.

Nahin, R.L., Barnes, P.M. and Stussman, B.J. (2016), “Expenditures on Complementary Health Approaches: United States, 2012”, National Health Statistics Reports, Number 95; DHHS publication; no. (PHS) 2016–1250.

Nguyen, C.V. (2011), “The impact of voluntary health insurance on health care utilization and out-of-pocket payments: new evidence for Vietnam”, Health Economics, Vol. 21 No. 8, pp. 946-966, doi: 10.1002/hec.1768.

Sommervoll, D.E. and Wood, G. (2011), “Home equity insurance”, Journal of Financial Economic Policy, Vol. 3 No. 1, pp. 66-85, doi: 10.1108/17576381111116768.

Thomas, K.J., Nicholl, J.P. and Coleman, P. (2001), “Use and expenditure on complementary medicine in England: a population based survey”, Complementary Therapies in Medicine, Vol. 9 No. 1, pp. 2-11, doi: 10.1054/ctim.2000.0407.

Van Damme, W., Leemput, L.V., Por, I., Hardeman, W. and Meessen, B. (2004), “Out‐of‐pocket health expenditure and debt in poor households: evidence from Cambodia”, Tropical Medicine and International Health, Vol. 9 No. 2, pp. 273-280, doi: 10.1046/j.1365-3156.2003.01194.x.

Van Doorslaer, E., O'Donnell, O., Rannan-Eliya, R.P., Somanathan, A., Adhikari, S.R., Garg, C.C., Harbianto, D., Herrin, A.N., Huq, M.N., Ibragimova, S. and Karan, A. (2006), “Effect of payments for health care on poverty estimates in 11 countries in Asia: an analysis of household survey data”, The Lancet, Vol. 368 No. 9544, pp. 1357-1364, doi: 10.1016/S0140-6736(06)69560-3.

Wagstaff, A. and Van Doorslaer, E. (2003), “Catastrophe and impoverishment in paying for health care: with applications to Vietnam 1993–1998”, Health Economics, Vol. 12 No. 11, doi: 10.1002/hec.776.

Xu, K., Evans, D.B., Kawabata, K., Zeramdini, R., Klavus, J. and Murray, C.J. (2003), “Household catastrophic health expenditure: a multicountry analysis”, The Lancet, Vol. 362 No. 9378, pp. 111-117, doi: 10.1016/S0140-6736(03)13861-5.

You, X. and Kobayashi, Y. (2011), “Determinants of out-of-pocket health expenditure in China”, Applied Health Economics and Health Policy, Vol. 9 No. 1, pp. 39-49.

Zhou, Y., Norton, E.C. and Stearns, S.C. (2003), “Longevity and health care expenditures: the real reasons older people spend more”, The Journals of Gerontology Series B: Psychological Sciences and Social Sciences, Vol. 58 No. 1, pp. S2-S10, doi: 10.1093/geronb/58.1.S2.

Further reading

Branson, J. and Knox Lovell, C.A. (2000), “Taxation and economic growth in New Zealand”, Taxation and the Limits of Government, Springer, Boston, MA, pp. 37-88, doi: 10.1007/978-1-4615-4433-3_3.

Leightner, J.E. (2008), “Omitted variables and how the Chinese Yuan affects other Asian currencies”, International Journal of Contemporary Mathematical Sciences, Vol. 3 No. 14, pp. 645-666.

Lukemeyer, A., Meyers, M.K. and Smeeding, T. (2004), “Expensive children in poor families: out‐of‐pocket expenditures for the care of disabled and chronically ill children in welfare families”, Journal of Marriage and Family, Vol. 62 No. 2, doi: 10.1111/j.1741-3737.2000.00399.x.

Acknowledgements

There was no funding for this paper and the author has no conflicts of interest.

The author appreciates Frazer McGilvray’s help with acquiring and setting up the data.

Corresponding author

Jonathan E. Leightner can be contacted at: jleightn@augusta.edu

Related articles