Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter September 27, 2014

Environmental policy and economic growth: the macroeconomic implications of the health effect

  • Jhy-hwa Chen , Jhy-yuan Shieh EMAIL logo and Juin-jen Chang

Abstract

This paper introduces health effects in an endogenous growth model with environmental concerns. To highlight the importance of health effects, we examine the time allocation of households in regard to leisure, labor, and health care, which play a crucial role in affecting the impacts of public abatement and emission taxation. We not only show that the health effect modifies the conventional consequences of environmental policy, but also thoroughly compare the effectiveness of these two distinct environmental policies. We also conduct transition and welfare analyses in a dynamic optimizing model which offers novel policy implications, given that the literature on health effects is silent on these issues.

JEL: H21; H23; I18; J22

Corresponding author: Jhy-yuan Shieh, Department of Economics, Soochow University, 56, Kuei-Yang St., Sec. 1, Taipei, Taiwan, Fax: +886-2-2382-2001, e-mail:

Acknowledgments

We would like to thank Managing Editor Arpad Abraham and two anonymous referees for their helpful suggestions and insightful comments on an earlier version of this paper. We would also like to express gratitude for the financial support provided by the National Science Council, Taiwan. Shieh and Chen would like to express their appreciation for the financial support provided by the Thematic Research Program-Sustainability Science, (Grant / Award Number: ‘AS-102-SS-A15’) Academia Sinica, Taiwan. Any remaining errors are, of course, our own responsibility.

Appendix

The Exact Derivatives of (13)

x=x=1Ωx>0,LS=LS=TσSΩ<0,
S=S=αTσSβΩL<0,Lτe=Lτe=1ββτeΩ<0,
τe=τe=1ββτeΩ>0,hS=hS=σhSσhh<0,
Lx=Lx=1Ωx<0,Ω=ϖ/βL>0.

The Proof of Proposition 1

We first prove the existence and uniqueness of the BGP equilibrium. From (15), we obtain: S*=g((1–β)/φτe)/δS>0. Substituting S* into (14) with x˙=0 further have:

x=Ξ(x)=Γ[(1β)1βτeβ1AL(x,S*)ε]1/β+ρ+(1θ)δkθ

By applying the fixed point theorem, the above equation tells us that since Lx=–1/Ωx<0, we must have a unique x*, which satisfies the BGP equilibrium.

The transitional dynamics of the system can be expressed by means of a phase diagram. It is clear from (13)–(15), that the slopes of loci x˙=0 and S˙=0 are:

Sx|x˙=0=[β(*+L*)θx*ε*[ρ+(1θ)δk]]S*[S*TσS{ε*[θx*(1θ)δkρ]+αηδS(1θ)}ψδkϖ(1θ)]x*0, and Sx|S˙=0=0,

implying that the S˙=0 locus is horizontal, while the x˙=0 locus can be either downward or upward sloping. By substituting (13) into (14) and (15), and then linearizing the resulting equations around the steady-state equilibrium, two characteristic roots of the dynamic system, denoted by υ1 and υ2, are:

υ1=δS<0 and υ2=ε*[ρ+(1θ)δk]βθx*(*+L*)ηβL*(1θ)θϖ>0.

This indicates that the dynamic system exhibits a saddle-path stability in which one root is stable and the other is unstable. Since there is a jump variable x in this dynamic system, the dynamic system will display a unique perfect-foresight equilibrium. Specifically, we can further obtain the general solution for (xt, St):

xt=x*+B1ev1t+B1ev2t and St=S*+v1x˙/xx˙/SB1ev1t,

wherex˙/x=v2,x˙/S=x*{{ε*[θx*ρ(1θ)δk]+αη(1θ)δS}S*TσSψ(1θ)δSϖ}[ηβ(1θ)L*θϖ]S* and B1 and B2 are undetermined coefficients. Since St can be recursively solved by (15), there is only one root governing the dynamics of the pollution stock.

The Comparative Statics of (16a) and Proofs of Propositions 2 and 3

From (13) to (15) with x˙=S˙=0, we obtain:

xτe=Φx*(θx*ϑ)ΔΘτeg[δ(*+L*)+εTσSgφτe]0,Lτe=ΦL*τeΔΘg'[δ*ϑ+βθTgσSx*φτe]0,
Sτe=Φδφτe2<0,τe=Φϑ*τeΔΘgL*[βθx*TσSgτeφϑδL*εTσSgτeφ]0,
hτe=Φσhsδφτe2σhh>0,γτe=αx*Φ(θx*ϑ)τeΓΔΘg[δ(*+L*)+εTσSgφτe]0,

where Δ=δS[βθx*(*+L*)–εℓ*ϑ]/Θ<0, ϑ=(1–θ)δk+ρ and Φ=(1–β)g′. On the other hand, the comparative statics concerning public abatement are given by:

xφ=x*(θx*ϑ)ΔΘΓ[θδϖ+εΦΓTσSφ2τe]0,Lφ=βθL*ΔΘ[δ*(θx*ϑ)ΓΦTσSx*φ2τe]>0,
Sφ=Φδφ2τe<0,φ=*ΔΘ{θδβL*(θx*ϑ)Γ+ΦTσS(θβx*εϑ)τeφ2}0,
hφ=Φσhsδφ2τeσhh>0,γφ=αε(θx*ϑ)ΔΘΓ[δ*(θx*ϑ)ΓΦTσSx*φ2τe]>0.

If the household’s time allocation is exogenously fixed (and the health effect is then absent), the impacts of emission taxation and public abatement are given by:

Sτe|exogL=(1β)gδφτe2<0,γτe|exogL=α[(1β)A/τe]1/βθβ<0.
Sφ|exogL=(1β)gδφ2τe<0,γφ|exogL=0.

The Proof of Proposition 4

Let ς and ξ be the co-state variables associated with the aggregate resource constraint and the law of motion for pollution. Thus, the optimal conditions for this optimization problem are given by:

(A1)cθη(1θ)Sψ(1θ)=ς, (A1)
(A2)ηc1θη(1θ)1Sψ(1θ)=(1φ)εy1LςεgeφyLξ, (A2)
(A3)εyL[(1φ)ς+ξgeφ(φy)2][σh(S,h)T1]=0, (A3)
(A4)(1φ)(1β)yςe+βgξφy=0, (A4)
(A5)ςy+egξφ2y=0, (A5)
(A6)ς˙ς=ρ+δkβk[(1φ)yegξφyς], (A6)
(A7)ξ˙ξ=ρ+δS+ψc1θη(1θ)Sψ(1θ)1ξεσSTL[(1φ)yςξegφy]. (A7)

By comparing (9a) with (A1) and (A2), we learn that λ=ς. As a result, utilizing (4a), (9c), (A2) and (A5) immediately leads to: φo=1–β>0. Moreover, substituting (4c), (A2)–(A6) into (A7) with ξ˙=0, the first-best emission tax can be obtained as: τeo=(MRS+σSTMPL)g(1β)(ρ+δS)y>0.

The Comparative Statics if Health Care is not only Time-Consuming but also Resource-Consuming

Given (6a) and (8a), the dynamic system can be summarized by the following four instantaneous relationships and two differentiating equations:

(A8)ηx=ε[(1β)1βτeβ1ALα]1/β, (A8)
(A9)σh(S,h,z)=1T, (A9)
(A10)[(1β)1βτeβ1ALα]1/βεσZ(S,h,z)=1T, (A10)
(A11)Tσ(S,h,z)=+L+h, (A11)
(A12)S˙=g(1βφτe)δSS, (A12)
(A13)x˙x=x+zρ(1αφ)[(1β)1βτeβ1ALε]1/β. (A13)

In the steady state, S˙=x˙=0. Thus, these six equations allow us to solve (L^,^,h^,z^,S^,x^) and the balanced-growth rate: γ^=(1φ)[(1β)1βτeβ1ALε]1/βx^z^δk.

Using (7), (6a), (8a), (15), and (A8)–(A13) with Z=zk, w=ε{[(1–β)/τe]1–βALα}1/βk and y={[(1–β)/τe]1–βALε}1/βk, we can obtain the following comparative statics:

γ^φ=αεx^[θ(x^+z^+δk)ρ]βΔ^ƛΓ{Φ[LxzS(1+zx)LS]τeφ2δLx[θ(x^+z^+δk)ρ]Γ}>0,γ^τe=αx^[θ(x^+z^+δk)ρ]βΔ^ƛΓτe{δ[(1+zx)(ετeLτeΦL^g)ετeLxzτe]+Φ[LxzSLS(1+zx)]φτe}0,

where Δ^=(δx^/ƛ){[θ(x^+z^+δk)ρ]/βθ(1+zx)}<0,=αTσz2σhhϖ^(σzzσhhσzh2)<0, and ƛ=(σzzσhhσzh2){θα^+βL^[θη(1θ)]}αTσz2σhh[θη(1θ)]>0. Note that to have a unique equilibrium which is locally determinate, we assume Δ^<0 such that the dynamic system exhibits saddle-path stability.

References

Aiyagari, S. R., J. C. Lawrence, and M. Eichenbaum. 1992. “The Output, Employment, and Interest Rate Effects of Government Consumption.” Journal of Monetary Economics 30: 73–86.10.1016/0304-3932(92)90045-4Search in Google Scholar

Ballard, C. L., and S. G. Medema. 1993. “The Marginal Efficiency Effects of Taxes and Subsidies in the Presence of Externalities.” Journal of Public Economics 52: 199–216.10.1016/0047-2727(93)90020-TSearch in Google Scholar

Barro, R. J., and X. Sala-i-Martin. 2004. Economic Growth. 2nd ed. New York: McGraw-Hill.Search in Google Scholar

Blanchard, O. J., and R. Perotti. 2002. “An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output.” Quarterly Journal of Economics 117: 1329–1368.10.1162/003355302320935043Search in Google Scholar

Bloom, D., D. Canning, and J. Sevilla. 2001. Economic Growth and the Demographic Transition. NBER Working Papers 8685, National Bureau of Economic Research.10.3386/w8685Search in Google Scholar

Bosi, S., and L. Ragot. 2013. “On the Optimal Control of Pollution in a Human Capital Growth Model.” Mathematical Economics Letters 1: 9–15.10.1515/mel-2013-0009Search in Google Scholar

Bovenberg, A. L., and R. A. de Mooij. 1997. “Environmental Tax Reform and Endogenous Growth.” Journal of Public Economics 63: 207–237.10.1016/S0047-2727(96)01596-4Search in Google Scholar

Bovenberg, A. L., and B. J. Heijdra. 2002. “Environmental Abatement and Intergenerational Distribution.” Environmental and Resource Economics 23: 45–84.10.1023/A:1020236812676Search in Google Scholar

Bovenberg, A. L., and S. Smulders. 1996. “Transitional Impacts of Environmental Policy in an Endogenous Growth Model.” International Economic Review 37: 861–893.10.2307/2527315Search in Google Scholar

Burtraw, D., A. Krupnick, E. Mansur, D. Austin, and D. Farrell. 1998. “The Costs and Benefits of Reducing Air Pollutants Related to Acid Rain.” Contemporary Economic Policy 16: 379–400.10.1111/j.1465-7287.1998.tb00527.xSearch in Google Scholar

Chang, J. J., J. H. Chen, J. Y. Shieh, and C. C. Lai. 2009. “Optimal Tax Policy, Market Imperfections, and Environmental Externalities in a Dynamic Optimizing Macro Model.” Journal of Public Economic Theory 11: 623–651.10.1111/j.1467-9779.2009.01423.xSearch in Google Scholar

Elbasha, E. H., and T. L. Roe. 1996. “On Endogenous Growth: The Implications of Environmental Externalities.” Journal of Environmental Economics and Management 31: 240–268.10.1006/jeem.1996.0043Search in Google Scholar

Fatás, A., and I. Mihov. 2001. “The Effects of Fiscal Policy on Consumption and Employment: Theory and Evidence.” INSEAD, mimeo.Search in Google Scholar

Grossman, M. 1972. “On the Concept of Health Capital and the Demand for Health.” Journal of Political Economy 80: 223–255.10.1086/259880Search in Google Scholar

Gutiérrez, M. 2008. “Dynamic Inefficiency in an Overlapping Generation Economy with Pollution and Health Cost.” Journal of Public Economic Theory 10: 563–594.10.1111/j.1467-9779.2008.00377.xSearch in Google Scholar

Hansen, A. C., and H. K. Selte. 2000. “Air Pollution and Sick-leaves.” Environmental and Resource Economics 16: 31–50.10.1023/A:1008318004154Search in Google Scholar

Hausmann, J. A., B. Ostro, and D. A. Wise. 1984. Air Pollution and Lost Work. NBER Working Papers 1263, National Bureau of Economic Research.10.3386/w1263Search in Google Scholar

Hettich, F. 1998. “Growth Effects of a Revenue-neutral Environmental Tax Reform.” Journal of Economics 67: 287–316.10.1007/BF01234647Search in Google Scholar

Howitt, P. 2005. “Health, Human Capital and Economic Growth: A Schumpeterian Perspective.” In Health and Economic Growth, edited by G. López-Casasnovas, B. Rivera, and L. Currais. MIT Press.Search in Google Scholar

Huang, C. H., and D. Cai. 1994. “Constant Returns Endogenous Growth with Pollution Control.” Environmental and Resource Economics 4: 383–400.10.1007/BF00692231Search in Google Scholar

Knowles, S., and D. P. Owen. 1995. “Health Capital and Cross-country Variation in Income per Capita in the Mankiw-Romer-Weil Model.” Economics Letters 48: 99–106.10.1016/0165-1765(94)00577-OSearch in Google Scholar

Krautkraemer, J. 1985. “Optimal Growth, Resource Amenities and the Preservation of Natural Environments.” Review of Economic Studies 52: 153–170.10.2307/2297476Search in Google Scholar

Lucas, R. E. 1988. “On the Mechanics of Economic Development.” Journal of Monetary Economics 22: 3–42.10.1016/0304-3932(88)90168-7Search in Google Scholar

Muller, N. Z., and R. Mendelsohn. 2007. “Measuring the Damages of Air Pollution in the United States.” Journal of Environmental Economics and Management 54: 1–14.10.1016/j.jeem.2006.12.002Search in Google Scholar

Mushkin, S. J. 1962. “Health as an Investment.” Journal of Political Economy 70: S129–S157.10.1086/258730Search in Google Scholar

Muysken, J., H. I. Yetkiner, and T. Ziesemer. 2003. “Health, Labour Productivity and Growth.” In Growth Theory and Growth Policy, edited by H. Hagemann and S. Seiter. London and New York: Routledge Press.Search in Google Scholar

OECD. 2008. OECD Environmental Outlook to 2030. Organisation for Economic Co-operation and Development, Paris.Search in Google Scholar

Ostro, B. 1983. “The Effects of Air Pollution on Work Loss and Morbidity.” Journal of Environmental Economics and Management 10: 371–382.10.1016/0095-0696(83)90006-2Search in Google Scholar

Ostro, B. 1987. “Air Pollution and Morbidity Revisited: A Specification Test.” Journal of Environmental Economics and Management 14: 87–98.10.1016/0095-0696(87)90008-8Search in Google Scholar

Ostro, B. 1994. Estimating the Health Effects of Air Pollutants: A Method with an Application to Jakarta. Policy Research Working Paper 1301, World Bank, Policy Research Department, Washington.Search in Google Scholar

Ostro, B., and S. Rothschild. 1989. “Air Pollution and Acute Respiratory Morbidity: An Observation Study of Multiple Pollutants.” Environmental Research 50: 238–247.10.1016/S0013-9351(89)80004-0Search in Google Scholar

Oueslati, W. 2002. “Environmental Policy in an Endogenous Growth Model with Human Capital and Endogenous Labor Supply.” Economic Modelling 19: 487–507.10.1016/S0264-9993(01)00074-8Search in Google Scholar

Palivos, T., and D. Varvarigos. 2014. Pollution Abatement as a Source of Stabilisation and Long-run Growth. mimeo.Search in Google Scholar

Pautrel, X. 2008. “Reconsidering the Impact of Pollution on Long-run Growth when Pollution Influences Health and Agents have a Finite-lifetime.” Environmental and Resource Economics 40: 37–52.10.1007/s10640-007-9139-ySearch in Google Scholar

Pautrel, X. 2009. “Pollution and Life Expectancy: How Environmental Policy Can Promote Growth.” Ecological Economics 68: 1040–1051.10.1016/j.ecolecon.2008.07.011Search in Google Scholar

Raffin, N. 2012. “Children’s Environmental Health, Education and Economic Development.” Canadian Journal of Economics 45: 996–1022.10.1111/j.1540-5982.2012.01724.xSearch in Google Scholar

Ricci, F. 2007. “Channels of Transmission of Environmental Policy to Economic Growth: A Survey of the Theory.” Ecological Economics 60: 688–699.10.1016/j.ecolecon.2006.11.014Search in Google Scholar

Romer, P. M. 1986. “Increasing Returns and Long-run Growth.” Journal of Political Economy 94: 1002–1037.10.1086/261420Search in Google Scholar

Russell, L. B., Y. Ibuka, and K. G. Abraham. 2007. “Health-related Activities in the American Time Use Survey.” Medical care 45: 680–685.10.1097/MLR.0b013e3180455782Search in Google Scholar

Schultz, T. W. 1961. “Investment in Human Capital.” American Economic Review 51: 1–17.Search in Google Scholar

Schwartz, J., and R. Repetto. 2000. “Nonseparable Utility and the Double Dividend Debate: Considering the Tax-interaction Effect.” Environmental and Resource Economics 15: 149–157.10.1023/A:1008314717413Search in Google Scholar

Strauss, J., and D. Thomas. 1998. “Health, Nutrition, and Economic Development.” Journal of Economic Literature 36: 766–817.Search in Google Scholar

USEPA. 1996. “The Benefits and Costs of the Clean Air Act, 1970–1990.” United States Environmental Protection Agency.Search in Google Scholar

van Ewijk, C., and S. van Wijnbergen. 1995. “Can Abatement Overcome the Conflict between the Environment and Economic Growth?” De Economist 143: 197–216.10.1007/BF01384535Search in Google Scholar

van Zon, A. H., and J. Muysken. 2001. “Health, Education and Endogenous Growth.” Journal of Health Economics 20: 169–185.10.1016/S0167-6296(00)00072-2Search in Google Scholar

WHO. 1983. Health Education in Self-care: Possibilities and Limitations. Report of Scientific Consultation. WHO: Geneva.Search in Google Scholar

WHO. 1998. The Role of the Pharmacist in Self-care and Self-medication. Report of the 4th WHO Consultative Group on the Role of the Pharmacist. WHO: Geneva.Search in Google Scholar

WHO. 2001. Macroeconomics and Health: Investing in Health for Economic Development. WHO: Geneva.Search in Google Scholar

Williams, III R. C. 2003. “Health Effects and Optimal Environmental Taxes.” Journal of Public Economics 87: 323–335.10.1016/S0047-2727(01)00153-0Search in Google Scholar

World Bank. 1993. World Development Report 1993: Investing in Health. New York: Oxford University Press.Search in Google Scholar

Xepapadeas, A. 2005. “Economic Growth and the Environment.” In Handbook of Environmental Economics, edited by K. G. Mäler and J. R. Vincent, 1219–1271. Vol. 3. Amsterdam: Elsevier Publishers Press.10.1016/S1574-0099(05)03023-8Search in Google Scholar

Zuidema, T., and A. Nentjes. 1997. “Health Damage of Air Pollution: An Estimate of a Dose-response Relationship for the Netherlands.” Environmental and Resource Economics 9: 291–308.10.1007/BF02441401Search in Google Scholar

Published Online: 2014-9-27
Published in Print: 2015-1-1

©2015 by De Gruyter

Downloaded on 28.3.2024 from https://www.degruyter.com/document/doi/10.1515/bejm-2014-0087/pdf
Scroll to top button