Health subsidies, prevention and welfare

• Published date: 01 December 2023
• Author: Luca Marchiori,Olivier Pierrard
• Date: 01 December 2023
• DOI: http://doi.org/10.1111/jpet.12583

Received: 8 September 2021

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Accepted: 1 March 2022

DOI: 10.1111/jpet.12583

ORIGINAL ARTICLE

Health subsidies, prevention and welfare

Luca Marchiori|Olivier Pierrard

Banque centrale du Luxembourg,

Luxembourg, Luxembourg

Correspondence

Luca Marchiori, Banque centrale du

Luxembourg, 2 boulevard Royal,

Luxembourg L‐2983, Luxembourg.

Email: luca.marchiori@bcl.lu

Abstract

People value healthy ageing but may underinvest in

health‐improving preventive care. This arises when

they ignore the beneficial effects of healthy ageing on

public health expenditures and hence on the tax

burden of future generations. This health externality

justifies public intervention. We build an overlapping

generations model with a government subsidizing

investment in health by the young generation and

paying the health care costs of the old generation. We

find that the welfare‐maximizing subsidy rate depends

positively on the health externality and the size of

health care costs, and negatively on the discount factor.

The subsidy rate should therefore be high when

prevention is cost‐effective and when the population

is careless about the future. Moreover, the welfare‐

maximizing subsidy rate is lower than the health‐

maximizing rate but higher than the capital‐

maximizing rate. This underlines the trade‐off for a

policy maker between health and economy.

1|INTRODUCTION

In this paper, we focus on one type of positive health externality, namely that young agents

ignore that healthy ageing (lower morbidity) reduces publicly financed curative health care

costs and hence the tax burden on the next generation. From a welfare point of view, this leads

to a private underinvestment in preventive health care justifying public intervention like

subsidies to prevention. Using an overlapping generations (OLG) setup, we analytically derive

the optimal subsidy policy. Our results also underline the trade‐off between health and

economy faced by a policymaker.

Why is this question important? First, one challenge of the graying society is to maintain

older people in good health (see e.g., EC, 2007; WHO, 2015), which requires preventive health

J Public Econ Theory. 2023;25:1304–1336.wileyonlinelibrary.com/journal/jpet1304

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© 2022 Wiley Periodicals LLC

care measures to improve future health status (Musich et al., 2016). Using OECD data, Wang

(2018) finds that preventive health care is currently under‐provided whereas curative health

care is over‐provided. This suggests that a change in the relative price of cares—for example,

through more subsidies on prevention—could improve the allocation of health expenditures

between prevention and cures. Second, the—absolute value of the—elasticity of curative costs

with respect to preventive actions may be large. Empirical studies show that prevention has a

considerable cost reducing effect by lowering morbidity, which again justifies the existence of

subsidization. Indeed, financial incentives may encourage healthy (e.g., dieting, physical

activity) or discourage unhealthy (e.g., smoking, alcohol) sustained behaviors and are found to

particularly support infrequent behaviors as vaccinations and screening (Mantzari et al., 2015;

Vlaev et al., 2019). Results on cost‐saving initiatives in the UK find that a return of 1.35 pounds

can be expected on every pound invested in flu vaccine or that screening is cost‐saving in the

short run for cervical cancer (below 5 years) and in the longer run for breast and colon cancer

(see WHO, 2014, for a review of these different studies).

1

Third, advanced countries spend

considerable resources on health. For instance, US national health expenditures as percent of

GDP increased from 5% in 1960% to 18% in 2015 (Catlin & Cowan, 2015). By 2028, US health

care should reach one fifth of the GDP. Although US has the highest health spending ratio

among developed countries, costs also exceed 10% in most European countries. One important

cost driver is the use of health care to live a longer healthy life, with costs proportionally larger

at older ages (WHO, 2018). Thus a cost–benefit analysis of subsidy on preventive care matters

not only from a medical but also from a public finance point of view.

To study the theoretical effects of health subsidy, we use an OLG framework with

households living for two periods. When young, households make consumption/savings

choices and undertake private health‐improving medical expenses, in short health investments.

These investments enhance individuals' health at old age, which provides utility and lowers the

need for publicly financed health care. There are thus two types of capital in the model and

both contribute to raise utility when old. Investing in physical capital provides earnings and

thus utility from higher old age consumption. Health investments improve health capital and

raise utility from a better health status. However, in contrast to physical capital, health capital

involves an externality. Indeed, young households invest in health capital to raise utility, not

caring that higher health capital will also reduce publicly financed health care when old and

hence the tax rate on the next generation. There is thus a rationale for the government to

subsidize medical expenses. The government taxes labor income to finance subsidies on health

investments by the young and health care needs of the elderly. A subsidy policy therefore

affects the economy through different channels. First, for given private health expenditures, a

higher subsidy raises taxation and depresses disposable income. This is the direct cost channel.

Second, for a given disposable income, a higher subsidy spurs health investments at the

expense of savings and consumption. This is the health investment channel. Third, increased

prevention today improves health status tomorrow, which reduces publicly financed health

care costs of the elderly. This is the health externality channel. A strong health externality

1

In general, prevention influences both morbidity and mortality. It directly decreases health care costs by lowering

morbidity, but also indirectly increases them by delaying mortality, with people continuing to consume health care

during the additional years of life (usually spent in poor health). Grootjans‐van Kampen et al. (2014) consider five

disease categories and show that in four out of five categories, prevention leads to health care savings without longevity

gains. Only prevention of highly fatal diseases (neoplasms) raises life expectancy and health‐related costs.

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indicates that prevention is on average effective at reducing future costs or alternatively that

prevention only targets specific cost‐saving initiatives.

We look at the steady state effects of a health subsidy on (i) physical capital, (ii) health status and

(iii) welfare. We show that the subsidy rate maximizing welfare depends positively on the health

externality and the size of health care costs, and negatively on the discount factor. The welfare‐

maximizing subsidy must therefore be large when prevention is very effective at reducing costs and

whenthepubliccostofhealthisimportant.Itmustalsobelargewhenprivateagentsdonotcare

enough about the future. This latter result relates to the empirical literature (see for instance Wang &

Sloan, 2018) showing that when individuals have an important degree of present bias, they are less

likely to invest in health. We also find that the subsidy rate maximizing welfare is larger than the rate

maximizing physical capital, but lower than the rate maximizing health status. Indeed, maximizing

welfare means we need good health, since health enters in the utility, but also a large capital stock to

generate enough production and consumption. Maximizing only health implies that we accept high

taxes and low consumption to pay for a very generous policy. Maximizing only capital means that we

accept a less generous policy and poorer health to lower taxes and stimulate savings. This key

message from a prevention policy—trade‐off between health and growth—is clearly robust to other

situations as for instance the containment policy in case of a pandemic (see, among many others,

Alvarez et al., 2020). To illustrate the theoretical findings,wepresentanumericalexamplebasedon

two advanced economies differing in the parameters of the health system structure. Moreover,

obtaining a full analytical characterization of the results obviously requires some specific modeling

choices. We therefore produce various numerical sensitivity analyzes and also discuss the

implications on our results of other types of health externalities (see Appendices A,C,D,andE).

Our paper relates to two branches of the health economics literature. One deals with

optimal health policy but disregards general equilibrium effects and macroeconomic

implications (Andersen & Bhattacharya, 2014; Cremer et al., 2012; Leroux et al., 2011)or

health externalities (Canta et al., 2016; Jack & Sheiner, 1997; Jaspersen & Richter, 2015). The

other one is concerned with the implications of health investments on the macro‐economy in

the presence of side‐effects of health capital but does not focus on optimal policy.

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Several

studies examine how health spending lowers mortality and affects growth in developing

countries.

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In Chakraborty (2004), public health investments raise longevity, which spurs

savings and raises the returns to human capital investment. In more wealthy countries, where

life expectancy is already high, health expenses increase more the quality of life than longevity.

Morbidity reduction may directly improve labor productivity (e.g., Fanti & Gori, 2011) and

some analyzes introduce both life expectancy and productivity effects (Kuhn & Prettner, 2016).

Only two other papers consider a health side‐effect describing how lower morbidity reduces

health‐related costs, which has been empirically shown to be important (Grootjans‐van

2

One exception is Atolia et al. (2021) who determine quantitatively the optimal combination of taxes and subsidies in a

neoclassical model and find that optimal subsidies increase along with the health externality on productivity. Our work

is complementary to theirs, as we find similar results (the optimal subsidy increases in the externality) using an

analytical approach and focusing on a different type of health externality.

3

These studies look at health‐induced longevity changes and are therefore also connected to a vast literature examining

the relationship between demographic factors and economic development. Many studies in this literature focus on the

implications of exogenous changes in longevity, reflecting, for example, policy changes, through capital accumulation

(Ito & Tabata, 2008) or through more complex mechanisms (like human capital accumulation or endogenous labor

supply, see Boucekkine et al., 2002; de la Croix & Licandro, 1999; Zhang et al., 2003). Other authors consider the effects

of endogenous life expectancy influenced by individual decisions (on health or education, see e.g., Blackburn &

Cipriani, 2002) or by aggregate variables (like environmental quality, see Balestra & Dottori, 2012).

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