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.
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)
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
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
implying that the
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):
The Comparative Statics of (16a) and Proofs of Propositions 2 and 3
From (13) to (15) with
where Δ=δS[βθx*(ℓ*+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:
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:
The Proof of Proposition 4
Let
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
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:
In the steady state,
Using (7), (6a), (8a), (15), and (A8)–(A13) with Z=zk, w=ε{[(1–β)/τe]1–βAL–α}1/βk and y={[(1–β)/τe]1–βALε}1/βk, we can obtain the following comparative statics:
where
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