Pollution, Private Investment in Healthcare, and Environmental Policy

Abstract

In this paper, we demonstrate that, in a two-period overlapping-generations model, the relationship between environmental taxation and economic activity (output level and growth) has an inverted-U shape when we take into account the detrimental impact of pollution on health and the individual decision of each working-age agent to improve her health.

We also demonstrate that the link between environmental tax and lifetime welfare also has an inverted-U shape, and that a tighter environmental policy might enhance economic activity while reducing steady-state lifetime welfare. Finally, we investigate the social optimum and the determinants of the optimal environmental tax.

I. Introduction

Is environmental policy harmful to economic activity, in terms of both output level and growth? Does a reduction in pollution imply such a heavy cost for the economy that the gains from a better environmental quality are not able to offset it? On a theoretical level, the answers are not clear-cut.

The aim of this paper is to contribute to the debate on one of the more striking features of pollution: its detrimental impact on health. In contrast to previous work in the field, where the impact of pollution on life expectancy (i.e., mortality) has been taken into account (see, among others, Jouvet et al., 2010; Mariani et al., 2009; Varvarigos, 2008; Pautrel, 2008, 2009b), we focus on the influence of pollution on illness and disability (morbidity) as a result of the development of chronic diseases such as cancer, diabetes, hypertension, heart disease, pulmonary conditions, and mental disorders.¹ There is a growing amount of empirical evidence for a link between pollution and chronic disease. This shows that even if pollution is not the main cause of these diseases, it is a contributory factor in their emergence and/or their deterioration.² In contrast to mortality, which affects mainly the old, illness and disability resulting from chronic disease primarily affect the working-age population, leading to significant losses in productivity and to rising health expenditure for the 30–50 age group. According to WHO (2004), in high-income countries, 56 percent of those suffering from some form of disease are people aged 15–59. As a result, the development of chronic diseases has a major economic impact in terms of labor productivity, labor supply, education, and savings, as shown by Suhrcke et al. (2006a).³ It also places a burden on healthcare and welfare systems. Devol and Bedroussian (2007), from the Milken Institute, estimate that, for the US, the seven most common chronic diseases represent a $277 billion annual expenditure on treatment and a loss in productivity equal to $1.1 trillion per year. Furthermore, chronic disease has major implications in terms of occupational choices, which cannot be supported (or funded) by the public healthcare system or insurance contracts.⁴

Rising health expenditure for working-age people and the increasing amount of time they have to devote to managing chronic disease are creating competition for resources that could be used in alternative ways, such as growth-promoting activities or final-production activities.⁵ The main contribution of this paper is to demonstrate that such competition for resources is a channel of transmission between environmental policy, economic activity, and welfare, when the detrimental impact of pollution on the health of the working-age population is taken into account.

To demonstrate this and to analyze its implications, we use a two-period overlapping-generations model, in line with previous research that has addressed intergenerational environmental issues,⁶ and we introduce an explicit link between the environment and health. Following empirical evidence, we assume that health is negatively influenced by pollution but is improved by the investment in health-enhancing activities made by each agent during her working life.⁷ Pollution is a by-product of final output production, and in a competitive economy the government taxes final output in order to limit pollution emissions.

Our first contribution is to demonstrate that if the detrimental effect of pollution on health status and the endogenous investment in health by the working-age population are taken into account, the link between environmental taxation and economic activity (final output level and growth) has an inverted-U shape. A tighter environmental policy has two opposite effects. First, because the environmental tax is imposed on final output, it reduces the rewards-to-production factor – the “drag-down effect”. Second, it reduces pollution, and therefore improves the health status of the working-age population. Agents reduce their investment in health-enhancing activities, and the resources that are thus made available are used to increase consumption and production. This second effect, called the “competition-for-resources effect”, is positive. For low values of environmental tax, the second effect offsets the first, and the environmental policy promotes output and its growth rate. Furthermore, when the productivity effect of a better health status is taken into account, the environmental tax is more likely to increase final output.

Our second contribution is to show that an inverted-U-shaped relationship between economic activity and an environmental tax also holds for steady-state lifetime welfare. Nevertheless, we demonstrate that under certain conditions concerning the share of consumption in utility and the share of physical capital in production, a tighter environmental policy might enhance economic activity while reducing steady-state lifetime welfare. This stems from the fact that, when the share of consumption in utility is higher than the relative part of physical capital in production, the negative impact of the drag-down effect is greater for lifetime welfare than for final output, and the positive impact of the competition-for-resources effect is lower for lifetime welfare than for final output. As a result, the negative impact of the environmental taxation exceeds the positive impact at a lower value for lifetime welfare than for final output.

Our third contribution is to show that if there is greater room for improvement in health status, then it is more likely that the environmental policy will promote economic activity and growth. This effect occurs when the rate of natural health decay is low, when the efficiency of healthcare spending is low, when the weight given to health in preferences is high, when the share of labor in final output is high, when the rate of natural purification of pollutants is low, when the polluting capacity of production technology is high, when the detrimental impact of pollution on health is high, and when the elasticity of pollution stock with respect to the net flow of pollution is high. Most of these criteria are satisfied in the most developed countries. Because the detrimental impact of pollution on health is well documented, our results show that an active environmental policy in these countries is highly likely to promote growth and output levels. In other words, the positive gains in terms of health and growth should be higher than the losses from factor rewards.

Finally, we investigate the social optimum and the optimal environmental tax. We demonstrate that if the the weight given to health in preferences is greater, if the elasticity of pollution stock is higher with respect to the net flow of pollution, and if the detrimental impact of pollution on health and/or the part of labor in production is higher, then the optimal environmental tax is higher.

The paper is organized as follows. The model is presented in Section II, and the competitive equilibrium and the impact of environmental taxation on the steady state are studied in Section III. In Section IV, the social optimum and the optimal environmental tax are investigated. Two extensions are examined in Section V: the AK endogenous growth and the impact of health on labor productivity. Conclusions are given in Section VI.

II. The Model

Let us consider an overlapping-generations model (as in Diamond, 1965) with endogenous preferences in health (as in van Zon and Muysken, 2001). A new generation is born at each date and lives for two periods. The number of individuals born at time t is L. Population is constant. Individuals are non-altruistic (i.e., the old do not care for the young, and the young do not care for the old). The preferences of an agent born in period t are represented by the following utility (from van Zon and Muysken, 2001):⁸

• (1)

Here, c_1t and c_2t+1 are consumption in youth and in old age, respectively, and h_t and h_t+1 are individual health status in youth and in old age, respectively. The parameter , where is the subjective discount rate of the agent. The parameter (respectively ) captures the relative importance of consumption (respectively health) in utility.⁹ Each young agent is endowed with one unit of time, supplying of this unit of time in final production and using the remaining time, , as an investment in healthcare activities to improve her health status.¹⁰ She earns a wage income , where w_t is the wage rate.

The individual health status of an agent born at period t evolves between period t and period t+1, depending on two opposing forces (Aisa and Pueyo, 2004). On the one hand, biological processes involve a natural decay in health simply as time passes. Following Grossman (1972) and Cropper (1981), we further assume that health depreciates over time as a function of the stock of pollution (denoted by S_t). On the other hand, the time invested in health-enhancing activities () mitigates against this deterioration. Therefore, for an agent born at t, individual health status evolves from period t to period t+1 as , where is the productivity scalar for health-enhancing activities.¹¹ The parameter measures the influence of pollution stock on the natural decay .¹²

A consumer, born at t, works during the first part of her life, consumes an amount c_1t, and saves the remainder of her revenue. The budget constraint of a young agent is

• (2)

where s_t denotes saving in youth. The budget constraint of an old person is

• (3)

where r_t+1 is the interest rate paid on savings held from period t to t+1.

Firms operate through perfect competition using physical capital and labor to produce a final good with a constant returns-to-scale Cobb–Douglas technology, , where Y_t is the aggregate output, K_t is the aggregate productive capital, N_t is labor, and . Here, is a productive scalar, assumed to be constant for the moment: . Capital depreciates fully in the production process.¹³

The stock of pollution S from period t to period t+1 increases because of the net flow of pollution in the current period t, denoted by P_t, and it decreases according to the rate of natural purification of pollutants . The net flow of pollution at time t depends on pollution emissions at time t, denoted by E_t, and on the abatement activities funded by the government, denoted by D_t, such that , where and . We follow Gradus and Smulders (1993, 1996), Oueslati (2002), and Varvarigos (2008), amongst others, by assuming that the function is homogeneous of degree zero and can be written as , where is the exogenous elasticity of the pollution stock with respect to the ratio of emissions to abatement services E/D. This specification is chosen for convenience. It is compatible with the case of endogenous growth, which we investigate in Section V,¹⁴ and it makes the model as simple and as analytically tractable as possible, without loss of generality (see footnote ¹⁵). We assume that polluting emissions arise from final production such that E_t=zY_t, where measures the polluting capacity of the technology. Abatement D_t is provided by the government as a public good and is financed by the environmental tax on the source of pollution Y_t, such that the public budget is balanced at each date: . The law of motion of the stock of pollution is therefore , where is the rate of natural purification of pollutants.¹⁵

III. Competitive Equilibrium

A representative agent born in period t maximizes her utility function, taking wages w_t, the interest rate r_t+1, the stock of pollution S_t, and the current health status h_t as given. She chooses consumption at both ages, c_1t and c_2t+1, and the proportion of time used in production:

• 

The first-order condition and the consumer constraints give saving and the allocation of time to production . Because , the health status of the old, h_t+1, is bounded to .¹⁶

Firms maximize their profit . The demand for capital is given by

• (4)

and the demand for labor is given by . The good-market clearing yields K_t+1=s_tL and the labor-market clearing equates labor demand N_t to labor supply : . Therefore, the competitive equilibrium can be defined by

• (5)

• (6)

• (7)

and . From equations (6) and (7), we obtain the expression for the time not invested in health-enhancing activities but rather allocated to final production with respect to health status h_t: . The higher the current health status h_t and the lower the current stock of pollution S_t, the lower the current time invested in health-enhancing activities .

The steady state is defined here as an equilibrium where physical capital, individual health status, pollution stock, final output, the wage rate, and the allocation of labor to production remain constant at any time at , , , , , and , respectively, with and

• (8)

• (9)

Consequently, health status and the time allocated to production are positively affected by the environmental tax . From equations (5) and (9), the steady-state value of the physical-capital stock is with . As ,¹⁷ we obtain the steady-state value of final output as a function of the environmental taxation : with and . Finally, the wage rate and savings at the steady state are respectively given by

• (10)

• 

Proposition 1. When endogenous investment in individual health status and the detrimental impact of pollution on health are taken into account, the relationship between the steady-state output and environmental taxation has an inverted-U shape. Below (respectively above) an environmental-tax level denoted byand defined as

• (11)

with, a tighter environmental taxation raises (respectively lowers) the steady-state level of output.

Proof: 

See Appendix A.

In equation (11), the first term on the left-hand side (LHS) represents the negative impact of the environmental tax on the output rate of growth (i.e., the drag-down effect), and the last term represents the positive impact of the environmental tax on the output rate of growth (i.e., the competition-for-resources effect).¹⁸ The environmental-tax level is the tax rate for which the drag-down effect and the competition-for-resources effect exactly offset each other.¹⁹

To understand the basic mechanism underlying Proposition 1, recall that

• (12)

Environmental tax influences the steady-state level of output through two channels: the direct impact of the environmental taxation on the rewards to labor (see overbrace Ia in equation 12) and the (indirect) impact on the allocation of labor in the manufacturing sector (see overbrace Ib in equation 12). The former (negative) is the well-known drag-down effect of the environmental tax that reduces factor rewards – captured by . The latter (positive) is a new channel of transmission resulting from the competition for resources between health-enhancing activities and production activities, which affects the supply of labor to the final-production sector . Because pollution has a detrimental impact on the evolution of individual health status, by reducing the net flow of pollution and therefore the stock of pollution, the environmental policy improves the individual health status of the agents. Consequently, each agent decides to reduce her investment in health-enhancing activities ( decreases) and to raise her labor supply to productive activities ( increases). In this way, the tighter environmental tax frees resources that were allocated to health-enhancing activities and these are now reallocated to production, leading to a higher level of steady-state output and steady-state physical capital. Consequently, the competition for resources between output production and health-enhancing activities, associated with the negative impact of pollution on health, is the origin of a new channel through which the environmental policy might promote economic activity.

When , changes in health status are independent of pollution, and therefore the investment of each agent in health-enhancing activities is not affected by the environmental tax (i.e., is independent of ). In such a case, the competition for resources is not affected by the environmental policy, and only the drag-down effect remains (i.e., the environmental policy is detrimental for growth). Equally, the competition-for-resources effect no longer holds when there is no endogenous investment in health-enhancing activities.

Corollary 1. Endogenous investment in health () and the detrimental impact of pollution on health () are two necessary conditions to obtain Proposition 1.

By considering the influences of parameters on the environmental-tax level , we can understand why these two opposing effects of the environmental policy lead to an inverted-U-shaped relationship between the environmental tax and the steady-state output level.

Proposition 2. When the negative impact of the environment on health and the endogenous decision of each agent to invest her resources in health-enhancing activities are taken into account, the environmental taxation will be more likely to improve the steady-state level of output if the rate of natural health decayis low, the efficiency of healthcare spendingis low, the weight of health in preferences () is high, the share of labor in final output () is high, the rate of natural purification of pollutantsis low, and the polluting capacity of production technology z is high.

Proof: 

Equation (11) gives the implicit expression of . Except for and , it is straightforward that , , , , , . From the theorem of the implicit function, we obtain , , , , , , and .

When the detrimental effects of a polluted environment on health are large, the gains made in terms of health by reducing pollutant emissions are very significant, and the competition-for-resources effect, which leads to an increase in labor supply, has a greater influence than the drag-down effect, which reduces factor rewards and, as a consequence, reduces saving and physical-capital accumulation. Nevertheless, these positive gains diminish with the increase in the tax rate because the possible improvements in health status are reduced as a result of the tax. At the same time, the losses from the reduction of factor rewards increase with the tax rate, such that for the environmental-tax level , they offset the gains, and a further increase in leads to a decrease in the steady-state output level. Consequently, the greater the possibilities for improving the environment and individual health status through environmental policy, the more beneficial the environmental policy is likely to be for the economy.

Because it is cumbersome to obtain analytically the influence of and on the tax level ,²⁰ we use a numerical application. We first calibrate the model, assuming that the length of each period is 30 years, which is usual in the literature. The first period covers ages 20–50, and the second period covers ages 50–80. We use the US economy as a benchmark. From De La Croix and Michel (2002), we choose and following the standard choice in the real business cycle (RBC) literature (i.e., and a quarterly psychological discount factor equal to 0.99). This implies that . We use the calibration by van Zon and Muysken (1997) for the values of and . The parameter , which measures the effectiveness upon health status of the time invested in health-enhancing activities, is chosen by analogy with Skinner et al. (2001), who note that nearly 20 percent of total medical-care expenditure provides no benefit to health. Thus, we consider that only 80 percent of the time invested in health-enhancing activities benefits health status (i.e., ). Furthermore, because the value of z seems to be important for determining the sign of the influence of and on (see footnote 20), we investigate a benchmark case z=0.3 and the case where z is very low (z=0.01). Finally, we set A (the productive scalar in the manufacturing sector) equal to 50 to obtain positive welfare at the steady state (denoted by ).²¹ The benchmark values of the parameters are summarized in Table 1, and the results of the numerical application are reported in Table 2 (where a variable with a hat and a star refers to a variable evaluated at the steady state for an environmental tax equal to ).

Table 1. Benchmark values of parameters

z					A		L
0.3	0.36	0.3	1/2	0.2	50	0.8	1	1	0.5	1.5

Table 2. Steady-statefor different values ofand

	Benchmark	26.55%	111.884	0.865	0.160	2.260	1.165
z=0.3		8.75%	130.462	0.892	0.165	6.859	1.427
		18.67%	119.359	0.871	0.161	3.213	1.278
		32.53%	106.645	0.864	0.160	1.844	1.079
		37.13%	102.831	0.867	0.160	1.616	1.012
		28.96%	111.474	0.878	0.162	2.089	1.151
		30.66%	111.448	0.889	0.164	1.936	1.144
		31.87%	111.633	0.890	0.166	1.799	1.141
		32, 74%	111.932	0.909	0.168	1.679	1.14
z=0.01		3.086%	145.85	0.965	0.178	0.648	1.589
		3.92%	147.07	0.977	0.180	0.510	1.60
		3.96%	148.75	0.988	0.182	0.504	1.612
		3.84%	149.26	0.991	0.183	0.521	1.617
		4.04%	148.05	0.984	0.182	0.495	1.605
		3.33%	149.75	0.991	0.183	0.329	1.622
		2.86%	150.626	0.994	0.184	0.244	1.631
		2.54%	151.15	0.996	0.184	0.194	1.637

Table 2 shows that for a very low value of z (0.01), an increase in (i.e., the influence of pollution stock on the natural decay of pollution) might reduce the threshold environmental-tax level . An increase in (i.e., the elasticity of pollution stock with respect to the ratio of emissions to abatement services) reduces . We can find the reason for this influence by examining the derivatives in footnote 20: a very low value for z leads to a high negative value of log z, which makes the derivatives negative. Because it seems reasonable to assume that such a very low level of pollution emissions rate z is unrealistic, we consider that the influence of and on is positive.

The influences of the parameters are summarized in Table 3. Finally, it is also possible to investigate the impact of environmental taxation on the steady-state lifetime welfare. This gives the following proposition.

Table 3. Parameter changes and responses of

						z
^aNegative for a very low value of z.
+	−	−	+	−	−	+	+^a	+^a

Proposition 3. There is an inverted-U-shaped relationship between the steady-state lifetime welfare of an agent (denoted by) and the environmental tax. Below (respectively above) an environmental-tax level denoted byand defined as

• (13)

with, a tighter environmental taxation raises (respectively lowers) the steady-state lifetime welfare.

Proof: 

See Appendix B.

Propositions 1 and 3 lead to the following corollary.

Corollary 2. If (respectively ), then (respectively ). Also, if , then . Therefore, if , when then and , when then and , and when then and . If , when then and , when then and , and when then and .

Corollary 2 means that the positive impact of a tighter environmental policy on the steady-state output level might have a detrimental impact on the steady-state lifetime welfare if the relative importance of consumption in utility () is higher than the relative part of physical capital in output production (). This follows from the fact that when , the negative impact of the drag-down effect is greater on lifetime welfare than on final output, and the positive impact of the competition-for-resources effect is lower on lifetime welfare than on final output (see the first and last terms on the right-hand sides of equations (13) and (11), respectively). As a result, the negative impact of the environmental taxation exceeds the positive impact at a lower value for lifetime welfare than for final output. Therefore, from Propositions 1 and 3, if , when a tighter environmental policy enhances both the steady-state output level and the steady-state lifetime welfare; when a tighter environmental policy enhances the steady-state output level but reduces the steady-state lifetime welfare; and when a tighter environmental policy diminishes both the steady-state output level and the steady-state lifetime welfare.

IV. Social Optimum and the Optimal Environmental Taxation

The purpose of this section is to investigate the determinants of the optimal environmental taxation with endogenous investment in individual health and a detrimental impact of pollution on individual health.

In a centralized economy, the central planner aims at maximizing the welfare of the agents, assuming that all generations are symmetric:

• 

As demonstrated in Appendix C, consumption at a young age and in old age are related:²² with . The optimal allocation of time to production is and the optimal stock of physical capital is . Consequently, the optimal final output is . Abatement activity is given by and the optimal stock of pollution in the steady state is . Consequently, the optimal value of the environmental tax, which can enable a decentralized economy to attain the optimal stock of pollution in the steady state, is

• (14)

This gives rise to the following proposition.

Proposition 4. The higher the weight of health in preferences (), the higher the elasticity of pollution stock with respect to the net flow of pollution (), the higher the detrimental impact of pollution on health (captured by) and/or the share of labor in production (), then the higher the optimal environmental tax is.

Proof: 

From equation (14), it is straightforward that , , , and .

Nevertheless, an optimal environmental tax is not sufficient to ensure an optimal steady-state equilibrium, because in a decentralized economy agents do not internalize the impact of their labor-supply decisions on final output and the net flow of pollution. Consequently, they do not supply enough time to output production. To obtain the optimal individual labor supply , the government has to subsidize health-enhancing activities at a rate of (see Appendix D)

• (14)

The environmental tax associated with the subsidy makes the steady-state decentralized equilibrium optimal.

V. Extensions

In this section, we extend the previous model in two directions. First, we investigate how our findings about the hump-shaped relation between the environmental taxation and final output in the long run might be extended to growth, when externalities in physical capital (see Romer, 1986) are introduced in the model of Sections II and III. Second, we add the impact of health on productivity, which is well-documented empirically (see Section I), to investigate how the results of Sections II and III are affected.

AK Endogenous Growth

In this section, we consider that external learning by doing (see Romer, 1986) exists,²³ such that the productivity scalar evolves as physical capital, , to obtain an interest rate independent of physical capital. Consequently, the final output becomes and the law of motion of physical capital is given by .

At the steady state, physical capital and output grow at a constant positive rate , that is, using equation (9)

• (14)

with .

Proposition 5. Under the assumption of a learning-by-doing source of growth (see Romer, 1986), the introduction of endogenous private expenditure in healthcare and the detrimental impact of pollution on health means that the relationship between the BGP growth rate and the environmental-tax level has an inverted-U shape. Below (respectively above) an environmental-tax level denoted byand defined as

• (15)

with, a tighter environmental taxation raises (respectively lowers) the BGP output growth rate.

Proof: 

The influence of the environmental taxation on the growth rate at the steady state is given by

• 

Consequently, if the last term on the right-hand side is positive: . Because the LHS of the inequality is a monotonic decreasing function of with and , there is a unique defined as , with (in order for to exist), such that for (respectively ) we have (respectively ).

Equation (15) defines the environmental-tax level for which its negative influence on the BGP growth rate (the first term on the LHS) equals its positive effect arising from the competition-for-resources effect (the second term on the LHS). For a tax level lower than , the positive impact of the environmental tax is greater than the negative impact, and an increase in the environmental tax raises the BGP growth rate. Conversely, for a tax level higher than , the competition-for-resources effect is too low for the environmental tax to increase growth.

Health Affects Labor Productivity

As emphasized in Section I, chronic diseases affect the economy through the huge losses in productivity that they create. As a result, it is expected that tighter environmental taxation can reduce this productivity loss by reducing pollution and increasing the health status of workers. To investigate how the association of the productivity effect with the competition-for-resources effect could further improve the beneficial impact of an environmental policy, we introduce the impact of health on labor productivity.

Following Gutiérrez (2008), we continue to consider that agents in poor health spend more on medical care when they are young and not when they are elderly. In contrast to Williams (2002, 2003), we do not assume that agents in poor health do not work. Rather, we consider that a better health status makes a worker more productive, and that absenteeism as a result of illness does not occur.²⁴ The technology to produce final output becomes , where measures the effect of health on labor productivity. The introduction of health-dependent labor productivity leaves the model unchanged, except for physical-capital accumulation (equation 5): . As a result, the steady-state value of physical capital becomes and the steady-state expression of final output is now with .

Proposition 6. When the effect of health on labor productivity is taken into account, the positive effect of an environmental tax on output level is increased, and the tax level at which a tighter environmental tax increases output level is higher. The environmental policy is more likely to increase final output.

Proof: 

The tax level, denoted by , for which , is defined by

• 

It is straightforward that for , . Furthermore, the LHS of the equation increases with because . Therefore, from the theorem of implicit function, we find that . Therefore, when .

VI. Conclusion

In this paper, we have investigated how environmental taxation affects the economy (output level and output growth, welfare) when the detrimental impact of pollution on health is taken into account and working-age individuals have to invest in healthcare to limit this impact. We have demonstrated that, in a two-period overlapping-generations model, the relationship between environmental taxation and economic activity (output level and output growth) has an inverted-U shape. This inverted-U-shaped relationship between the environmental tax and economic activity is the result of a positive effect arising from the competition for resources between the final output sector and the healthcare sector, which offsets the detrimental drag-down effect for low values of the environmental tax. Thus, a tighter environmental tax is more likely to increase (rather than decrease) output level and output growth when health is very pollution-sensitive, when the weight of health in preferences is high, when the polluting capacity of the production technology is high, and when the rate of natural purification of pollutants is low. Furthermore, when the productivity effect of better health status is taken into account, the environmental tax is more likely to promote final output. We have also demonstrated that the link between environmental taxation and lifetime welfare has an inverted-U shape, and that a tighter environmental policy might enhance economic activity while reducing steady-state lifetime welfare. Finally, we have investigated the social optimum and the determinants of the optimal environmental tax.

The main policy implication of our findings is the need to continue and reinforce efforts to reduce pollution, for example, in economies such as China and other Asian countries (Malaysia, Vietnam, etc.), where the detrimental effects of pollution on health are the highest and are predicted to increase significantly and where production processes generate high pollution emissions and the health sector is not efficient. Even in the high-income countries of North America and Europe, where production is less polluting and healthcare spending is more efficient, efforts to curb pollution should be pursued and strengthened; OECD (2008) forecasts that pollution emissions will continue to rise in the future with increasing negative effects on health. In both cases, there would be a greater scope for individual health-status improvements through a tighter environmental policy, and our results suggest that the expected positive impacts of such a policy would more than offset the detrimental effects. Nevertheless, our results also highlight that the welfare implications of any environmental policy should be carefully taken into account to avoid the situation where there is a negative impact on welfare from the environmental taxation while economic activity is increased.

We have also highlighted the need for a further investigation of the link between the environment, health, and economic activity. Indeed, a simple two-period overlapping-generations framework does not capture all the implications of an important feature of chronic disease (i.e., its persistent effect over decades). This has major implications in terms of social-security funding (see Section I) and intergenerational redistribution. It could also affect the long-term behavior of the agents, not only in terms of leisure, but also in terms of consumption (“brown” and “green” consumption), and in terms of time preferences. This could, in turn, reinforce the expected positive effects of the environmental policy, in terms of both output (level and growth) and lifetime welfare. Such a potential and persistent influence of tighter environmental policy on health appears to be a promising area of empirical and theoretical investigation.

Appendix A. Influence of the Environmental Tax on the Steady-State Output in Competitive Equilibrium

The influence of environmental tax on the steady-state level of output is given by

• 

The influence of environmental tax on the steady-state level of output is positive if

• ((A.1))

Because the LHS of the inequality is a decreasing monotonic function of with and , there is a unique under which the inequality is verified. This is denoted by and is defined by with for the second term on the LHS being positive, that is, to obtain a solution for . For and , we have and , respectively. When , the LHS of the inequality is independent of and negative, and therefore we have . When , the condition (A1) is never verified whatever the value of , and therefore

Appendix B. Influence of the Environmental Tax on Steady-State Lifetime Welfare in Competitive Equilibrium

The lifetime welfare along the BGP is defined by the lifetime utility function (1) evaluated along the BGP. That is, using equations (2), (3), (4), (8), (9), (10), and , we obtain with

• 

and . Furthermore, with

• ((B.1))

Therefore, if , that is, from equation (B1), if . Because the LHS of the inequality is a monotonic decreasing function of with and , there is a unique under which the inequality is verified. This is denoted by and is defined as with . When and ) we have and , respectively.

Appendix C. The Optimum

In a centralized economy, the central planner aims to maximize the welfare of the agents, assuming that all generations are symmetric:

• 

The Lagrangian can be written as

• 

The first-order conditions are

• ((C1))

that is, and

• ((C2))

• ((C3))

• ((C4))

Equations (C2) and (C4) give and from (C1), we obtain . Therefore, , and consequently the market equilibrium gives , i.e.,

• 

In the same way, the market equilibrium can be written as , that is, . Consequently, , i.e.,

• ((C5))

Finally, equation (C3) gives (i.e., ). From equation (C5), , , , and .

Appendix D. Subsidy to Health-Enhancing Activities

The competitive equilibrium is rewritten, assuming that the government subsidizes the agents’ health-enhancing activities by paying a subsidy, , towards the opportunity cost of health-enhancing activities (i.e., the foregone wage ). This is funded by a lump-sum tax denoted by a_t. The budget constraint for a young agent born at period t becomes . The maximization of lifetime utility gives . Because government budget constraints require , we obtain and the individual labor supply is .

In the steady-state equilibrium, and are similar to equations (8) and (9) with the term replaced by . The subsidy of health-enhancing activities, which enables replication of the optimal allocation of time between health-enhancing activities and production (denoted by ), is such that , that is,

• 

Footnotes

• 1

  According to the World Health Organization (WHO, 2004, 2005), chronic diseases are responsible for 60 percent of all deaths worldwide, and they are a major source of disability, especially in developing countries. Nevertheless, they also affect developed countries (Suhrcke et al., 2006b; Zhang et al., 2009). Devol and Bedroussian (2007) found that more than half of all Americans (55.8 percent) were suffering from one or more chronic diseases in 2003.

• 2

  According to Briggs (2003), about 8–9 percent of the total disease burden can be attributed to pollution in developed countries. Amongst others, Brook et al. (2004), Rajagopalan et al. (2005), Lang et al. (2008), and Lee et al. (2007) show that different types of pollution are associated with cardiovascular diseases, diabetes, and obesity; for details, see Pautrel (2009a), which is the working paper version of this paper.

• 3

  For the US in 2003, Davis et al. (2005) estimated that 55 million workers out of 148 million, aged 19–64, reported an inability to concentrate at work because of their own illness or that of a family member; 69 million workers reported missing days because of illness.

• 4

  As emphasized by Mullahy and Robert (2008), increasing levels of physical activity are now viewed as a means to improve health outcomes. The US Department of Health and Human services advises that, in order to be in good health, a person should do 150 minutes of physical activity at a moderate level or 75 minutes at a vigourous level each week. In their study, based on the American Time Use Survey carried out by the Bureau of Labor Statistics, Russell et al. (2007) noted that 11.3 percent of American adults (in 2003–2004) reported spending time (mean, 108 minutes) on activities related to health during the day before their interview, and 5.6 percent (86 minutes) reported taking medicine, giving themselves a shot, exercising, or having therapy for medical reasons.

• 5

  Competition for resources in the relation between health and growth has been studied in several articles (for details and references, see Dormont et al., 2011). Nevertheless, most of these contributions view better health as an increase in life expectancy. Empirically, Dormont et al. (2006) find that there are changes in morbidity, which induce savings that more than offset the increase in spending as a result of the aging population.

• 6

  For example, John and Pecchenino (1994) analyze the potential conflict between economic growth and the maintenance of environmental quality when consumption degrades environmental quality while investment in environmental maintenance promotes it. Also, John et al. (1995) investigate the effects of environmental taxation by distinguishing between the horizons of the agents and of the economy. For models with non-renewable resources, see Agnani et al. (2005), Kemp and Long (1979), and Mourmouras (1991, 1993).

• 7

  Because we consider that the agents are suffering from chronic diseases that require medical care when they are young, we do not assume that agents with poor health spend more on medical care when they are elderly, as Gutiérrez (2008) does. In contrast to Williams (2002, 2003), we do not assume that agents who are ill do not work.

• 8

  For simplicity, we use logarithmic preferences. A constant relative risk aversion (CRRA) utility function could be used, as in Agénor (2008), but this would make the model more complex, with no improvement in the qualitative results. Proof upon request.

• 9

  Green preferences are not included, because it is assumed here that health status is affected by pollution.

• 10

  We could assume that there is a sector that produces healthcare services using labor, and therefore that a part of labor is allocated to manufacturing production and a part is allocated to healthcare production. We would find the same qualitative results (proof upon request). Consequently, what we call “investment in health-enhancing activities” could be viewed as healthcare expenditure. Our modeling has the advantage of leading to a simpler exposition of the model and the results. Finally, the results are not modified when leisure time is introduced. Proof upon request.

• 11

  Note that we model a linear relationship between the health-enhancing activities and the evolution of health status, which might not be empirically relevant. As demonstrated by Skinner et al. (2001), “nearly 20 percent of total Medicare expenditure appears to provide no benefit in terms of survival, nor is it likely that this extra spending improves the quality of life.” Our assumption is made for simplicity. Note also that other authors (e.g., Bednarek et al., 2008) have considered a more general dynamic for health status, but they have not introduced the role of pollution in health dynamics.

• 12

  We impose to investigate the absence of a detrimental impact of pollution on health (i.e., ). Nevertheless, it is expected that (i.e., the higher the stock of pollution, the higher the detrimental effect of pollution), even if there is no empirical evidence for such a linear relationship.

• 13

  The production process is over the course of a generation. If the annual depreciation rate is 10 percent (which is empirically relevant), then 96 percent of the capital stock is depreciated over the course of a 30-year generation. Therefore, we assume that capital is fully used up in the production process (for further details, see De La Croix and Michel, 2002).

• 14

  Such a specification of the net flow of pollution is used in most of the continuous-time endogenous growth models that deal with the environment (for references, see the survey by Xepapadeas, 2005) because it gives a constant stock of pollution in the long run, while the emissions and the abatement services grow constantly.

• 15

  The specification of the net flow of pollution that we have chosen leads the dynamics of the stock of pollution to be independent of economic activity at all times. The use of a specification as in Varvarigos (2008), which makes the dynamics of the stock of pollution dependent on final output, does not modify the qualitative results but makes the model more complex (proof upon request). We have not used the linear specification of the net flow of pollution from John and Pecchenino (1994), where , because here abatement is public and requires the assumption , which is not easy to justify economically. Furthermore, it does not allow us to investigate the case with endogenous growth because E_t−D_t are not constant along the balanced growth path (BGP), and therefore the stock of pollution explodes in the long run.

• 16

  See van Zon and Muysken (1997, p. 5) for a justification of the health-status boundary.

• 17

  Note that .

• 18

  Note that we impose to obtain a solution for (see Appendix A).

• 19

  Note that the Bell relationship between tax rate and output implies a Laffer curve for the environmental taxation (proof upon request). We thank an anonymous referee for highlighting this point.

• 20

  We have and , because .

• 21

  Welfare at the steady state is defined by the lifetime utility function (1) evaluated at the steady state. It increases when A increases (see Appendix B).

• 22

  A bar denotes the optimal value.

• 23

  Following Romer (1986), production factors remain paid at their marginal productivity after environmental tax cost.

• 24

  We take into account presenteeism (i.e., a worker is present but with reduced productivity) rather than absenteeism (i.e., a worker absent), because this accounts not only for a worker's health but also for the health of the worker's family. For the US in 2003, Davis et al. (2005) estimated that 55 million workers out of 148 million workers, aged 19–64, reported an inability to concentrate at work because of their own illness or that of a family member.