環境政策與內生成長 - 政大學術集成

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(1)國立政治大學經濟學系博士論文. 環境政策與內生成長 Environmental Policies and Endogenous Growth. 指導教授：賴景昌教授研究生：朱. 巡. 撰. 中華民國一百零一年十二月.

(2) 謝辭感謝我的指導教授賴景昌老師。在博士生涯中，老師對我的影響絕對是全面性的。除了知識上的傳授，老師對教學的高標準要求、做研究的態度、看學術的視野、甚至待人處事的方法都為我們樹立了良好的典範。其中最讓我欽佩的是即使老師已有相當傲人的學術成就，對追求學問的熱忱仍是我們這些後輩學者所遠不能及。但老師也告訴我們做學問從不要有壓力，常說的一句口頭禪「快樂的做研究」每每在我寫論文遇到困難時給我重新出發的動力。另外也要感謝老師在求學期間提供了良好的研究環境與充足資源，讓我能更無後顧之憂地完成論文的撰寫。感謝我的口試委員周登陽老師、洪福聲老師、陳明郎老師、張俊仁老師與賴育邦老師，在百忙中願意抽空審閱我的論文，指正疏漏並提供許多寶貴建議，令論文更臻完整，謹此致謝。我也非常感謝陳鎮洲老師與賴育邦老師在學校亦師亦友的提攜與照顧。感謝志興學長從不吝嗇分享經驗，給予我諸多指導與幫助。另外感謝映安學姐、祥玉、緁妶、晉祥、惠婷、振維、冠任與平河，互相扶持打氣並為漫長的博士生涯增添色彩。謝謝老爸、老媽、老哥和家裡的三隻傻貓，家裡因為有你們充滿了歡笑，回到家總是讓我心情愉悅，將煩惱拋諸腦後。最後當然要謝謝竹小君一路走來的陪伴與支持，生命有了你們太美好，我將此論文獻給你們。. 朱巡 2012 年 12 月.

(3) 摘要環境保護可以與經濟成長兼顧嗎？本論文試圖回答這個問題。我們發展三個包含環境外部性的內生成長模型，透過不同管道來證明較嚴格的環境政策可能同時改善環境品質與促進經濟成長。更具體言之，在第二章中我們假設中間財廠商向國外以固定價格購買污染要素，此情況下環境政策將存在正的成長率效果；在第三章中我們考慮一個疊代內生成長模型，主張假如環境稅收移轉給年輕世代的部分很大，環境稅有可能提高經濟成長率；在第四章中我們證明當較好的環境品質會提高民眾儲蓄意願，提高環境稅可以促進經濟成長。本論文的主要結果與近二十年來崛起的文獻認為環境保護政策也可能有利經濟成長相一致。.

(4) Abstract Can environmental protection be compatible with economic growth? dissertation we attempt to answer this question.. In this. We develop three frameworks that. incorporate the elements of endogenous growth and environmental externalities.. We. argue that, via different channels, implementing a tighter environmental policy could simultaneously be beneficial to the environmental quality and the long-term economic growth rate.. More specifically, in Chapter II we present the positive growth effect of. environmental policies by assuming that the intermediate firms import the polluting inputs from abroad at a fixed price.. In Chapter III, we consider an OLG framework. and demonstrate that if the portion of tax revenues transferred to young generations is large, it is possible for an environmental tax to boost the growth rate.. In Chapter IV,. it is shown that when a cleaner environment can induce people more willing to save for future consumption, increasing the environmental tax could stimulate growth. The main findings of this dissertation join the literature advocating a beneficial growth effect of an environment protection policy in the last two decades..

(5) Contents ___________________________________________________________ Chapter I :. Introduction References. Chapter II :. Abatement R&D, Market Imperfections, and Environmental Policy in an Endogenous Growth Model 2.1. Introduction. Chapter III :. 1 5. 6 6. 2.2. The model 2.3. Public versus private abatement 2.4. Quantitative results 2.5. Concluding remarks. 10 15 20 28. Appendix References Figures. 31 32 35. Intergenerational Welfare and Pareto-improving Environmental Policies 3.1. Introduction. 39 39. 3.2. The model 43 3.3. Competitive equilibrium 48 3.4. Policy effects without environmental externality 49 3.5. Environmental externality and Pareto-improving policies 56 3.6. Concluding remarks Appendix References Figures Chapter IV :. Chapter V :. 59 61 65 68. Endogenous Time Preference Depending on the Environmental Quality: Economic Growth and Policy Implications 4.1. Introduction. 70 70. 4.2. The model 4.3. Policy implications 4.4. Extensions 4.5 Concluding remarks Appendix. 73 75 80 82 84. References. 85. Conclusions. 88.

(6) Chapter I ___________________________________________________________ Introduction Can environmental protection be compatible with economic growth?. Over the. last few decades environmentalists and economists have engaged in this fundamental question.. However, the answer to this question is hardly conclusive.. While earlier. theories suggest the answer is no, Bovenberg and Smulders (1995) demonstrate that the environmental taxation may stimulate economic growth by assuming that a better environmental quality is beneficial to input productivity.. Since then there has been a. rapidly increasing body of researches that advocate a beneficial growth effect of an environment protection policy. to this debate.. In this dissertation we make an attempt to contribute. We provide three frameworks incorporating the elements of economic. growth and environmental externalities.. The central goal is to bring up some new. channels that are not explored in previous studies, via which a tighter environmental policy may stimulate long-term economic growth. In Chapter II, we first pay our attention to an important channel in environmental economics, namely the pollution abatement.. In standard models on environment and. economic growth, pollution is usually treated as an input or a by-product of output. As endogenous growth theory requires output and consumption to grow unlimitedly, it is essential to abate pollution within a survival level in the long run.. According to. previous studies on the relationship between pollution abatement and economic growth, the research and development (R&D) of the abatement technology/knowledge is conducted only by the public sector.. This setting, however, is not very realistic. because both real-life observations and empirical evidences show that private and public investment in abatement technology coexist.. 1. Indeed, we often observe that.

(7) abatement technologies are developed in a private upstream sector and then are sold to downstream polluting industries.. Motivated by this discrepancy between theories. and actuality, in Chapter II we construct a model that is able to consider both possibilities of public and private abatement R&D. The contribution of the framework is twofold.. First, we highlight the positive. growth effect of environmental policies by assuming that the intermediate firms import polluting inputs from abroad at a fixed price.. We demonstrate that, as the. environmental tax raises, the value of abatement knowledge increases so that more abatement knowledge would be invested.. In other words, the higher environmental. tax reduces the pollution by way of an accumulation of abatement R&D, with the amount of polluting inputs unchanged (because the import price is fixed).. Therefore,. the environmental quality is better with the same level of polluting inputs.. Given. that a cleaner environmental quality is beneficial to productivity, the environmental tax has an unambiguously positive effect on economic growth. Second, within this framework we are able to make a comparison of economic performances under the regimes of private and public abatement investment.. In. particular, we compare the relative superiority in terms of economic growth and social welfare among various regimes.. It is found that a higher growth rate can be. achieved if the abatement R&D is conducted privately with the government subsidy. In addition, we show that the economic performance under the private provision of abatement knowledge depends mainly on the monopoly power of the polluting firms. This is because the incentive for the environmental R&D sector to engage in R&D increases with the intermediate firms’ profit.. As the monopoly power is greater, the. benefit arising from the private implementation of abatement is larger, and thus more (private) R&D activities will be conducted, resulting in a higher growth rate.. Our. results highlight that market imperfections play an important role when integrating 2.

(8) abatement investment with private incentives. In Chapter III, we investigate the linkage between environmental quality and economic growth in an overlapping generations (OLG) model developed by Diamond (1965).. The degradation of the environment often requires a period of time.. Existing generations who pollute the environment today may not live long enough to bear the consequences of environmental deterioration in the future.. An environment. protection policy, therefore, should have different effects on the welfare level of different generations.. An infinitely-lived agent model, as presented in Chapter II,. cannot reflect this effect.. Hence we resort to the OLG model.. We show that the growth effect of the environmental tax depends on how the tax revenue is split out among young and elders.. When the environmental tax goes up, it. reduces the young agents’ wage income, and therefore the young generation will tend to reduce both consumption and savings.. On the other hand, with part of the tax. revenues being transferred to young generations, they will save more with a higher environmental tax since they can receive more transfer income.. If the portion of tax. revenues transferred to young generations is large, it is possible for an environmental tax to stimulate the growth rate. The last channel that may result in a positive growth effect of environmental policies is related to an endogenous time preference depending on the environmental quality, which we plan to present in Chapter IV.. The notion that as environmental. quality changes people will become more patient (or impatient) is first brought up by Pittel (2002).. A plausible reason to illustrate the idea might be to think that if the. environment is going to be severely damaged and below the physical condition for life, then saving would become meaningless.. Therefore, for a rational individual it is. very nature to alter the time preference with a different environmental quality. However, in the previous literature on environment and economic growth, this effect 3.

(9) is surprisingly overlooked.. Hence, in this chapter we will make an effort to examine. the implications of such an endogenous time preference on the growth effect of environmental protection policies. More specifically, we develop an endogenous growth model featuring the capital externality proposed by Romer (1986) and Lucas (1988), in which the agent's time preference is endogenously determined by the environmental quality.. We will show. that, in the absence of an endogenous time preference, there is a trade-off relationship between environmental quality and economic growth.. By contrast, in the presence. of an additional external effect arising from environmental quality on time preference, increasing the environmental tax may boost the balanced growth rate, implying that environmental protection can be compatible with economic growth.. Moreover, we. demonstrate that the famous Pigouvian tax rate may be inefficient in the presence of the environmentally endogenous time preference. Finally, the main results of each chapter and some implications to the theories are summarized in Chapter V.. 4.

(10) References Bovenberg, A. L. and S. Smulders (1995), Environmental quality and pollution-augmenting technical change in a two-sector endogenous growth model, Journal of Public Economics 57, 369-391. Diamond, P. A. (1965), National debt in the neoclassical growth model, American Economic Review 55, 279-293. Heijdra, B. J., J. P. Kooiman and J. E. Ligthart (2006), Environmental quality, the macroeconomy, and intergenerational Economics 28, 74-104.. distribution,. Resource. and. Energy. Lucas, R. E., Jr. (1988), On the mechanics of economic development, Journal of Monetary Economics 22, 3-24. Pittel, K. (2002), Sustainability and Endogenous Growth. Cheltenham, UK: Edward Elgar. Romer, P. (1986), Increasing returns and long-run growth, Journal of Political Economy 94, 1002-1037.. 5.

(11) Chapter II ___________________________________________________________. Abatement R&D, Market Imperfections, and Environmental Policy in an Endogenous Growth Model 2.1. Introduction An important environmental problem for policymakers is how to reconcile sustainable growth with limited pollution.. On the one hand, endogenous growth. theory requires most economic factors to grow unlimitedly; while on the other hand, if pollution, an input or a by-product of output, grows to infinitely large, any life or economic activities could hardly exist.. To ensure sustainable growth, therefore, it is. essential for pollution to abate within a survival level in the long run.. In US, for. example, the estimated total annual abatement expenditure represents between 1.5% and 2.5% of GDP (Berman and Bui, 2001). Recent studies dealing with the relationship between pollution abatement and environmental growth, such as van Ewijk and van Wijnbergen (1995), Bovenberg and Smulders (1995, 1996), Fullerton and Kim (2008), treat abatement as technologies or knowledge that could be accumulated and developed in a separate sector (i.e., the environmental R&D sector).. 1. Since knowledge is non-rival and has the. characteristic of a public good, the costs associated with the use of abatement knowledge as an input are zero, while knowledge creation and accumulation, in contrast, require rival inputs and are costly. 2. This implies that, as stressed in. Bovenberg and Smulders (1995), in a perfectly competitive market, abatement R&D could not be rewarded so that no innovation in abatement technologies would be 1. Alternatively, some studies treat abatement spending as a flow variable which cannot be accumulated. See Gradus and Smulders (1993), Ligthart and van der Ploeg (1994), Smulders and Gradus (1996), and Bovenberg and de Mooij (1997). 2 See Smulders (1995) for a detailed discussion. 6.

(12) undertaken without the government’s intervention.. Therefore, the strand of this. literature essentially assumes that abatement R&D activities are publicly conducted by the government.3 In reality, however, we often observe that private and public abatement activities coexist.. Moreover, it is usually observed that abatement technologies are developed. and produced in a private upstream sector, and then sells abatement equipment (or blueprints) to downstream polluting industries (OECD, 2000; Greaker and Rosendahl, 2008).. In US, the private abatement investment is even more than the public. abatement investment (OECD, 2007, table 3).. Based on these observations, it is. quite fair to say that a satisfactory model should be able to consider both possibilities of public and private abatement R&D.. This is what we aim to do in this chapter.. To be more precise, we build up a theoretical framework which enables us to make a comparison between the economic performance under the regimes of private and public abatement investment. Another key feature of our model is that we introduce imperfect competition in the intermediate good market.. As mentioned above, private abatement R&D. requires incentives, which are not available in a perfect market because the competitive firms would not be left with any quasi-rent for abatement R&D.. Hence,. we should resort to a different market structure, such as an imperfectly competitive market.. In the 1980s, several studies (e.g., Hart, 1982; Mankiw, 1985; Blanchard. and Kiyotaki, 1987) noted that market power in the private sector plays a crucial role in the performance of government policy.. More recently, Judd (2002) has also. argued that imperfect competition is a key feature of dynamic modern economies. 3. One exception is van Ewijk and van Wijnbergen (1995), in which the accumulation of abatement capital is costless (a byproduct of the accumulation of human capital); thus private abatement is conducted even without policy intervention. As is evident, our model structure is completely different from theirs. Furthermore, van Ewijk and van Wijnbergen (1995) do not deal with public abatement investment. 7.

(13) The empirical evidence, on the other hand, suggests that polluting industries are often equipped with monopoly power (Beccarello, 1996; Considine, 2001).. To reflect the. observed facts, a considerable body of studies develop environmental economic models which take market imperfections into account (e.g., Fullerton and Metcalf, 2002; Greaker and Rosendahl, 2008; Chang et al., 2009). Following the footstep of these studies, this chapter develops an environmental endogenous-growth model that features market imperfections.. More specifically, the. market structure we consider is characterized by three vertically-integrated sectors. Abatement technologies are developed in an upstream sector, which sells the abatement knowledge (ideas) to the intermediate sector.. The intermediate sector. which generates pollution can earn positive profit by exhibiting monopoly power, but it has to pay fees to the upstream sector for the right to use the abatement knowledge. The perfectly competitive downstream sector produces a single final output by employing intermediate inputs.. Under such a setting, we are able to deal with. various regimes including public abatement (hereafter, GA), private abatement without tax recycling (PA), and private abatement with tax recycling (PAR). Moreover, we compare the relative superiority in terms of economic growth and social welfare among various regimes.. In particular, we highlight whether market. imperfections play an important role in determining the relative superiority. An interesting issue is whether the private provision of abatement knowledge leads to a higher growth rate than public abatement.. Our analysis shows that the. answer crucially depends on two factors, namely, the monopoly power of the polluting firms and the type of government spending.. We find that the greater the. degree of the firms’ monopoly power, the larger will be the benefit arising from the private implementation of abatement.. The reason for this result is that the incentive. for the upstream sector to engage in R&D is precisely determined by the intermediate 8.

(14) firms’ profit.. It is also found that growth will be enhanced if the government. distributes its tax revenues to boost (or directly engage in) abatement R&D.. This. finding implies that if environmental tax revenues are used to provide public goods or other private services, a subsidy on private R&D abatement will possibly be a good choice to achieve higher economic growth and social welfare. The analysis of this chapter is also related to recent studies on the effect of environmental taxation on economic growth.. The conventional wisdom in the. literature (e.g., Huang and Cai, 1994; Ligthart and van der Ploeg, 1994; Grimaud, 1999) is often that there is an unavoidable conflict between economic growth and the conservation of the environment in the economy.. However, in recent years a. growing body of literature that proposes a positive growth effect of environmental taxation has accumulated.. For example, in their frequently cited article, Bovenberg. and Smulders (1995) find that environmental taxation has an ambiguous effect on economic growth by assuming that environmental quality is beneficial to input productivity.4. In departing from this strand of the literature, our analysis assumes. that the pollution inputs are purchased from abroad at a non-bargaining price. Accordingly, a higher environmental tax will reduce the pollution by way of an accumulation of abatement R&D, but the polluting inputs will remain unchanged. Since an environmental tax does not decrease the level of polluting inputs (and thereby the marginal productivities of other inputs), it undoubtedly spurs economic growth through the positive environmental productivity effect. The remainder of this chapter proceeds as follows.. Section 2.2 describes the. model and solves the firms’ and households’ optimization problems. Section 2.3 4. Other justifications contributing to a positive (ambiguous) environmental tax effect on economic growth include a positive externality of abatement activities (Smulders and Gradus, 1996), elastic labor supply (Hettich, 1998; Chen et al., 2003), the international accumulation of environmental assets (Ono, 2003), tax revenues recycled to subsidize intermediate goods R&D (van Zon and Yetkiner, 2003; Nakada, 2004), and the existence of an indeterminate equilibrium path (Itaya, 2008). 9.

(15) deals with three distinct regimes associated with different abatement policies. Section 2.4 presents our simulation results and compares the growth rates and the welfare levels among the three regimes.. Section 2.5 provides some concluding. remarks.. 2.2. The Model The economy we consider is composed of three parts: the households, the production sectors, and the government.. The production sectors are characterized by. a perfectly competitive market for final goods and a monopolistically competitive market for intermediate goods.. Moreover, intermediate firms invest in abatement. R&D to improve pollution reduction technology.. In what follows, we in turn. describe the structure of the economy.. 2.2.1. Production sectors In line with Benhabib and Farmer (1994) and Farmer and Guo (1994), the production side of the economy consists of two sectors: a perfectly competitive final good sector and a monopolistically competitive intermediate goods sector.. There is. a continuum of intermediate goods yi , i ∈ [0, 1] , which are used by a single representative firm to produce a final good Y .. Following Dixit and Stiglitz (1977),. we specify that the production of the final good exhibits the following constant returns-to-scale technology: Y =  ∫ yi  0 1. 1−θ. di  . 1 1−θ. ,. θ ∈ [0, 1) .. (2.1). As we will show later, θ indexes the degree of monopoly of the intermediate good firms. Let π Y denote the profit of the final good firm and qi be the price of the ith 10.

(16) intermediate good in terms of final output.5. The maximization problem of the final. good firm can be expressed as: 1 1−θ 1 1−θ Max π Y =  ∫ yi di  − ∫ qi yi di ,  0  0 yi 1. (2.2). The first-order condition for this problem yields the demand function of the ith intermediate good:. yi = (qi ) Y . −. 1 θ. (2.3). It is quite clear from (2.2) that the demand function of the ith intermediate good has a constant price elasticity 1 / θ .. When θ approaches zero, intermediate goods are. perfect substitutes in the production of the final good, implying that the intermediate goods sector is perfectly competitive.. However, if 0 < θ < 1 , intermediate good. firms face a downward-sloping demand curve so that they can exert monopoly power. Since our main concern lies in the mutual interactions among environmental externality, abatement R&D, and market imperfections, in the following analysis we focus our attention on the case in which 0 < θ < 1 . Based on the fact that the final market is perfectly competitive, substituting (2.3) into (2.2) and imposing the zero-profit condition yields:. ∫q 1. 0. i. θ −1 θ. di = 1 .. (2.4). The technology for producing the ith intermediate good is given by: yi = A( N )ki ei α. 1−α. β l yi , A′( N ) > 0 ,6. (2.5). where A is an environment-productivity function, N is environmental quality, and ki , l yi and ei are the capital, labor and emission inputs used by the ith intermediate 5. It should be noted that the final good is treated as the numeraire in this . It is worthy noting that in a monopolistic competition market, although the production function is an increasing-returns-to-scale form, it does not necessary imply negative profits as long as the monopoly power θ is large enough (see, e.g., Benhabib and Farmer, 1994). In fact, as will be seen later in our numerical example, the profit-output ratio of an intermediate firm is around 3.6%. 6. 11.

(17) firm, respectively.. To reflect the positive production externality arising from the. environmental quality, (2.5) specifies that the output level of the intermediate goods rises with a better natural environment.. The profit function of the ith intermediate. firm π i can then be expressed as: π i = qi yi − rki − mei − ω l yi − τ P pi ,. (2.6). where r is the capital rental rate, ω is the real wage, m is the price of the polluting input, and τ P denotes a tax (or price of permits) that the government levies on actual pollution pi .. We assume that the intermediate firm purchases polluting input ei. from abroad so that the input price m is taken as given (e.g., the polluting input can be treated as if it were petroleum).. 2.2.2. Environmental quality. The pollution generated in the production process of the ith intermediate firm is of the form:.  e ε pi =  i  , H 1. (2.7). where H is the stock of abatement knowledge, and 1/ ε ( ε > 0 ) is the elasticity of pollution production with respect to “abated polluting inputs”.. In (2.7), pollution is. specified to be positively related to polluting input ei and negatively related to abatement knowledge H.. Accordingly, the total pollution P in the economy is the. sum of polluting emissions generated by all intermediate firms:. P = ∫ pi di . 1. (2.8). 0. Following Fullerton and Kim (2008), the natural environment is treated as a renewable resource, and can hence be specified to grow and deplete in the following manner: 12.

(18) N = bN (1 − N ) − P ,. (2.9). where a dot denotes the rate of change with respect to time, b is a parameter, and the term bN (1 − N ) reflects the regeneration capacity of the environment, which might initially increase with a larger N but eventually decline when N exceeds a threshold value.. (2.9) indicates that a rise in the level of pollution is associated with a decline. in environmental quality in the next period.. In the steady state, the environmental. quality remains constant over time since pollution equals the regeneration capacity of the environment ( P = bN (1 − N )) . We restrict our analysis to a symmetric equilibrium in which ki = k , ei = e ,. l yi = l y , pi = p , π i = π , yi = y , and qi = q for all i. have Y =  ∫ yi  0 1. 1−θ. di  . 1 1−θ. = y.. As a result, from (2.1) we. With y = yi and qi = q , the profit of the final good. firm stated in (2.2) then can be expressed by π Y = (1 − q) y .. Given that the final. good sector is perfectly competitive, the profit of the representative final good firm earns zero profit (i.e., π Y = 0 ) in equilibrium.. Accordingly, the zero-profit. condition in the final good sector π Y = 0 requires q = 1 .. Furthermore, let K , E ,. and L y denote the aggregate capital stock, aggregate emission, and aggregate labor hired by the intermediate firms. L y = ∫ l yi di = l y . 1. 0. Then, we have: K = ∫ k i di = k , E = ∫ ei di = e , 1. 1. 0. 0. As a consequence, the intermediate firms’ first-order conditions. can be arranged as:. (1 − θ )α. Y =r, K. (1 − θ )(1 − α )ε. (1 − θ ) β. (2.10). Y = τ P + εmHP ε −1 , P. Y =ω . Ly. (2.11) (2.12). 13.

(19) (2.10)-(2.12) indicate that, given the environmental quality and abatement knowledge, firms equate the marginal product of the capital, labor and pollution to their respective marginal cost.. 2.2.3. Households There is a continuum of identical infinitely lived households, each of which derives positive utility from both consumption C and environmental quality N. Population is stationary and normalized to unity for simplicity.. The representative. household utility is given by:. W =∫ ∞. (CN η )1−σ − 1 exp[− ρt ]dt , 1−σ 0. (2.13). where W is the discounted lifetime utility of the representative household, ρ is the subjective time preference rate, σ is the intertemporal substitution elasticity, and η denotes the weight in terms of the utility attached to the environment or, as proposed by Fullerton and Kim (2008), the “consumption externality” in relation to the environment. Each household is endowed with a fixed amount of labor L , which is allocated to production between the intermediate goods ( L y ) and research ( LH ). that labor is homogeneous and perfectly mobile across sectors. must, as a result, hold.. A unique wage rate. The representative household receives income by supplying. labor and capital services to firms.. Under the GA regime, it receives profits π in. the form of dividends and lump-sum transfers G from the government.7 capital income tax rate τ K is levied on the capital rentals.. The budget constraint under PA and PAR regimes will be introduced in Section 2.3.2. 14. Finally, a. Accordingly, the budget. constraint faced by the representative household can be expressed as:. 7. We assume.

(20) K = (1 − τ K )r K + ω L + π + G − C .8. (2.14). The optimum conditions for the representative household with respect to consumption and physical capital are: C −σ N η (1−σ ) = λ ,. (2.15). λ / λ = ρ − (1 − τ K ) r ,. (2.16). where λ is the shadow price of the private capital stock.. 2.2.4. Abatement R&D activity As noted earlier, pollution abatement technologies are regarded as knowledge and can thus be accumulated over time.. The creation of knowledge requires efforts. and time so that innovation and invention are acts of investment (Smulders, 1995). In line with Romer (1990) and Jones (1995), we assume that new ideas are developed by the labor input and the existing stock of ideas.. To be more precise, abatement. knowledge H is specified to be created in the following manner: H = δ LH H ,. (2.17). where δ is a productivity parameter and LH denotes the labor input for R&D activities. In our model, for long-run growth to be feasible and sustainable, the balanced growth path (BGP) in the steady state is characterized by: Y C K H E = = = = =g, Y C K H E. N = P = 0 ,. (2.18). where environmental quality and pollution are limited in a physical sense, and all other economic variables grow at a common constant endogenous growth rate g.. 2.3. Public versus Private Abatement 8. We do not consider a labor income tax because the total labor supply is fixed. 15.

(21) Two possible facts concerning the R&D activities and the government budget constraint are considered in this section.. First, the R&D activities can be conducted. by either private firms or the government.. Second, if the R&D activities are engaged. in by private firms, the government may or may not subsidize the R&D activities. Based on these two kinds of possibility, our analysis can be classified into three different regimes: public abatement (GA), private abatement without tax recycling (PA), and private abatement with tax recycling (PAR).. Since the government budget. constraint varies with each of the three regimes, the BGP may display quite contrasting results among these three regimes.. In what follows, we discuss three. types of regimes in turn. 2.3.1. Public abatement Under the GA regime, the R&D activities are engaged in by the government. Under such a situation, the balanced budget constraint faced by the government can be expressed as follows: G + qH H = τ K rK + τ P P ,. (2.19). where new abatement knowledge H is produced according to (2.17), and qH is the price of abatement knowledge relative to final goods.. (2.19) states that the. government receives its revenues in the form of capital taxes τ K rK and pollution taxes τ P P to finance its provision of lump-sum transfer payments to the household G and public abatement investment q H H . The government budget constraint (2.19) is consistent with the Fullerton and Kim (2008) specification, in which abatement knowledge is regarded as a public good and can be used freely by firms.. Notice that since labor is perfectly mobile, the. marginal revenue product of labor should be the same between two sectors.. (1 − θ ) β. Y ∂H = qH . Ly ∂LH. That is:. (2.20). 16.

(22) Using (2.17), (2.19), and (2.20) together with the household budget constraint yields the resource constraint of the economy: K = Y − C − mE .. (2.21). Imposing the conditions for a BGP and defining the following transformed variables: h = H / K , c = C / K , w = ω / K , φ = G / K , and τ = τ P / K , the macroeconomy along the BGP equilibrium can then be described by the following set of equations: g∗ =. [. ]. (1−α )ε ∗1−α ∗ β 1 (1 − τ K )(1 − θ ) A( N ∗ ) P ∗ h Ly − ρ , σ. (2.22). g ∗ = δ ( L − L∗y ) ,. (2.23). (1 − θ )(1 − α )εA( N ∗ ) P ∗ (1 − θ ) βA( N ∗ ) P ∗ c ∗ = A( N ∗ ) P ∗. (1−α ) ε. (1−α )ε. 1−α. 1−α. h∗. β. ε. L∗y = τP ∗ + εmh ∗ P ∗ ,. (2.24). β. h∗. 1−α. h∗. (1−α )ε. L∗y = w∗ L∗y ,. β. (2.25) ε. L∗y − g ∗ − mh ∗ P ∗ ,. (2.26). P ∗ = bN ∗ (1 − N ∗ ) ,. τ K (1 − θ )α A( N ∗ ) P ∗. (2.27) (1−α ) ε. 1−α. h∗. β. L∗y + τP ∗ = φ + w∗ ( L − L∗y ) ,. (2.28). where the superscript “*” stands for the steady-state value. The macroeconomic model expressed in the above seven equations determines seven unknowns, i.e., h ∗ , c ∗ , P ∗ , N ∗ , L∗y , w∗ , and g ∗ .. Since the system is in a. nonlinear form and is too complicated to obtain a closed-form solution, we thus present our results via numerical simulations.. 2.3.2. Private abatement R&D This sub-section deals with both the PA and PAR regimes. regimes, the R&D activities are undertaken by private firms. 17. Under these two. As a result, we first.

(23) need to formulate how abatement knowledge is produced in the R&D sector.. To. achieve this purpose, in line with the standard R&D literature including Romer (1990) and Jones (1995), we assume that the three sectors in this economy are vertically integrated.. Moreover, abatement technologies are developed and produced in an. upstream (R&D) sector, which hires labor to engage in innovation activity and then sell the abatement knowledge (ideas) to the intermediate (polluting) sector.. The. downstream sector produces a single final output by employing a set of intermediate inputs. Following the literature of R&D-based endogenous growth models, e.g., Romer, (1990) and Barro and Sala-i-Martin (2004), two important assumptions are made. First, there is free entry into the upstream (R&D) sector so that the R&D firms earn zero profit.. Second, an R&D firm charges a price for its ideas at which the. intermediate firms are indifferent between buying (to produce) and not buying (to leave the market).. More specifically, the license fee for new abatement knowledge. must be equal to the net profit that a monopolistic firm can extract, that is:9 qH =. π 10 . H. (2.29). The profit function of the R&D firms π H can be written as:. π H = q H H − (1− s )ω LH ,. (2.30). where s is the subsidy rate for the labor employment of the R&D firm. Substituting (2.17) into (2.30) and imposing the zero-profit condition yields:. δ q H H = (1 − s ) ω .. (2.31). 9. According to Kamien and Tauman (1986), a patentee can license her invention to an oligopolistic industry by means of a fixed fee or a per unit royalty. It should be noted that in this chapter the price of abatement knowledge can be regarded as a fixed license fee that an intermediate firm should pay to R&D firms in exchange for the right to use abatement knowledge. 10 In the standard R&D-based endogenous models, the intermediate firms make a one-off payment to R&D firms for the right to use the knowledge forever after. However, in our model the intermediate firms need to make flow payments to use the abatement knowledge in every period. 18.

(24) It should be noted that, under the PA regime, the government does not subsidize R&D activities, and hence this regime corresponds to s = 0 .. However, under the PAR. regime, the government provides R&D subsidies, and hence this regime is associated with s ≠ 0 .. We now deal with these two regimes in turn.. 2.3.2.1 Private abatement R&D without tax recycling Under the PA regime, the government neither invests in R&D nor subsidizes it (i.e., s = 0 ).. Hence, the government budget constraint is given by:. G = τ K rK + τ P P .. (2.32). Since the profit of the intermediate firms is allocated to pay for the use of abatement knowledge, no dividends are distributed to the households.. Accordingly, the. household budget constraint can be rewritten as: K = (1 − τ K )rK + ω L + G − C .. (2.33). Based on the above conditions, it can be shown that the resource constraint reported in (2.21) still holds in the PA regime.. At the BGP equilibrium, the economy is. described by (2.22)-(2.27) together with the following condition (mathematical derivations are provided in the Appendix): δ [1 − (1 − θ )(α + β ) − (1 − θ )(1 − α )ε ] * δ (1 − ε )mh ∗ P ∗ g = Ly − . (1 − θ ) β w∗ ε. ∗. (2.34). 2.3.2.2. Private abatement R&D with tax recycling Under the PAR regime, the government subsidizes the private abatement R&D instead of directly conducting the R&D activities.. Hence, the government budget. constraint becomes:. G + sω LH = τ K rK + τ P P .. (2.35). After some manipulations, (2.34) and (2.35) can be modified as:. 19.

(25) δ [1 − (1 − θ )(α + β ) − (1 − θ )(1 − α )ε ] ∗ δ (1 − ε )mh ∗ P ∗ Ly − , (1 − s ∗ )(1 − θ ) β (1 − s ∗ ) w∗ ε. g∗ =. τ K (1 − θ )α A( N ∗ ) P ∗. (1−α ) ε. 1−α. h∗. β. L*y + τP ∗ = φ + s ∗ w∗ ( L − L*y ) .. (2.36). (2.37). The BGP economy can then be described by (2.22)-(2.27), (2.36), and (2.37), where eight unknowns h ∗ , c ∗ , P ∗ , N ∗ , L∗y , w∗ , g ∗ , and s ∗ are solved in eight equations.. 2.4. Quantitative Results A numerical analysis is presented in this section to trace how the growth rate and welfare level will react following a change in an environmental policy under the three regimes.. To construct an illustrative example, we choose benchmark parameter. values that are within the plausible ranges used in the literature.. Table 2.1 lists the. benchmark parameter values, and some interpretations concerning these parameter configurations should be provided here.. First, in line with Fullerton and Kim (2008),. we specify the environment productivity function as the form A( N ) = N γ and set the following parameters: γ = 0.77 , α = 0.24 , b = 0.04 , η = 0.7 .. Second, the values. σ = 1.5 , β = 0.67 , and ρ = 0.05 are based on the calibration exercises in Lucas. (1990) and Stokey and Rebelo (1995).. The monopoly power index θ = 0.33 is. adopted from Judd (1997), in which he considers the values θ ∈ [0.1,0.4] . Accordingly, the resulting profit ratio in our economy is 3.6%, and is conformable to the profit ratio of the typical US industry; see, e.g., Basu and Fernald (1997) and Guo and Lansing (1999).11 Third, to reflect the model’s plausibility we choose τ K = 0.16 (based on the estimate reported by Auerbach, 1996) and φ = 0.03 as policy parameters. 11. We choose the GA regime as our baseline economy when calibrating. 20. This in.

(26) turn implies that the government’s spending as a proportion of output is 17.4%, and hence this numerical value lies within the reasonable interval in the literature; see e.g., Gali (1994).. Fourth, the pollution tax relative to the capital stock τ = τ P / K is set. Table 2.1 Parameter. Value. Parameter. α. 0.24. β. σ. 1.5. ρ. ε. 0.6. η. γ. 0.77. τK. 0.16. τ. 30. δ. m. 2.5. L. b. 0.04. θ. φ. Value 0.67 0.05 0.7 0.33 0.03 0.01 20. as 30 so that the ratio between the tax revenues and output is about 23.2%.12. Fifth,. as for the pollution conversion parameter, while Bovenberg and Smulders (1995) simply assume that ε is equal to 1, Fullerton and Kim (2008), however, relax this assumption and allow ε to vary from 0.6 to 0.9.. A relatively low value of ε. means that the elasticity of pollution production with respect to “abated polluting inputs” is high.. That is, raising the level of polluting inputs will not only increase. pollution, but will also accelerate the generation process.. More specifically, the. investment in abatement knowledge will be more important if the elasticity is higher. To highlight the role of abatement investment, we set ε = 0.6 as our parameter value. Finally, the values of (m, δ , L ) are calibrated so that the balanced growth rate is 3.12%, which is close to the average growth rate for the past 30 years in the US.. 2.4.1. Comparison of three regimes 12. Supposing K = 1, in the steady state we have P = 0.00133 and Y = 0.1721. Accordingly, the ratio of pollution tax revenues to output is (30)(0.00133)/0.1721 = 23.18%, which is slightly higher than the 17.8% in Fullerton and Kim (2008). As pointed out by Fullerton and Kim, it is inappropriate to compare this pollution share with existing pollution taxes, since actual pollutants are restricted by mandates so that the pollution share should also include scarcity rents resulting from the restrictions. 21.

(27) Table 2.2 presents the key endogenous variables in the benchmark case.. Our. goal is to compare the steady state growth rate and the welfare level under the three regimes.. As shown in Table 2.2, in the GA regime, the steady state growth rate is. about 3.12%.. In the PA regime, the government switches the abatement spending to. a lump-sum transfer, and the intermediate firms are forced to purchase the license fee for abatement knowledge from the R&D firms. growth rate declines to 1.73% in response.. Under such an arrangement, the. However, if the tax revenues are recycled. to subsidize the R&D sector, the growth rate of 4.51% is ranked the highest among the three regimes.. In addition, as shown in Table 2.2, the rank of the abatement. knowledge among the three regimes is the same as that of the balanced growth rate. The intuition behind this coincident ranking follows from the fact that, as indicated in (2.17), an accumulation of abatement knowledge unambiguously enhances economic growth. Table 2.2 Environmental. Pollution. quality. Abatement. Growth. knowledge. rate (%). Welfare. GA. 0.9656. 0.00133. 0.4506. 3.124. -49.1803. PA. 0.9720. 0.00101. 0.3416. 1.732. -67.0781. PAR. 0.9600. 0.00153. 0.5786. 4.506. -36.3432. However, by comparing the value of pollution under the three regimes, it may be of little surprise that a higher abatement investment is associated with more pollution. The economic intuition behind this result can be explained as follows.. Other things. being equal, a better environment (less pollution) should be achieved if the firm has access to more abatement knowledge.. However, once the government directly. provides or indirectly subsidizes abatement knowledge, the cost of pollution-reducing activities will decline.. Cheaper abatement knowledge gives the firms an incentive to. 22.

(28) use more polluting inputs, which worsen the environmental quality.. In our model, it. seems that the latter effect dominates the former, and thus abatement knowledge and pollution receive the same ranking among the three regimes. We now turn to compare the level of welfare under the three regimes.. We focus. on the welfare along the BGP, denoted by W ∗ , which is calculated by using (2.13) and (2.26): W∗ =. 1  −1 1 C01−σ N ∗η (1−σ ) −  ,  ∗ 1 − σ  (1 − σ ) g − ρ ρ. where C0 = [ A( N ∗ ) P ∗. (1−α )ε. 1−α. h∗. β. (2.38). ε. L∗y − g ∗ − mh ∗ P ∗ ]K 0 , C0 and K 0 are the initial. consumption and capital stock, respectively. 13. The numerical values of social. welfare under the three regimes are reported in the last column of Table 2.2.. It is. clear that the ranking of the level of welfare among the three regimes is the PAR regime, the GA regime and the PA regime in that order.. The policy implication is. that, given the baseline parameter values, the growth rate and welfare are the lowest if abatement activities are conducted privately without government intervention. Nevertheless, they could be both enhanced once the government engages in public abatement or provides incentives for private abatement R&D.. If the latter is the case,. the growth rate and welfare could achieve the highest levels. 2.4.2. Parameters with policy implications It should be noted that the numerical simulations regarding the growth rate and welfare are examined only under the baseline parameter values.. An interesting. concern is how our simulation results are related to the values of the parameters.. To. this end, in what follows we propose three relevant parameters that need to be considered by the policy-makers.. 13. Without loss of generality, we set K0 = 1 in our numerical model. 23.

(29) 2.4.2.1. Market imperfection An early but insightful point of view by Schumpeter (1942) is that more competition would erode the monopolistic rents, and thus reduce the incentive to undertake R&D activities.. We stand in line with this perspective and extend it to an. economy in which R&D investment is used to control the pollution.. To be more. specific, in our model the decentralized economy suffers from two market failures. The first concerns the environmental externality.. Pollution harms human health and. productivity, but is not accounted for by the polluting firms.. The second has to do. with the market imperfections regarding the supply of intermediate goods.. However,. these imperfections can become the motivation for people to engage in R&D in the case where the polluting firms need to pay a license fee to use abatement technologies, but not in the case where there is public provision of free abatement knowledge.. In. other words, only in the regime of private abatement (PA and PAR) can the second market failure (imperfect competition) remedy the first market failure (the environmental externality).. Based on this observation, market imperfections play a. critical role when integrating abatement investment with private incentives. Figure 2.1 exhibits the effects of varying the monopoly power parameter ( θ ). A rise in θ is associated with an increase in both the balanced growth rate and the level of welfare under both the PA and PAR regimes.. To explain this result, by. substituting (2.29) into (2.30) we obtain π = (1 − s )ω LH , where a higher profit implies more employment of research workers.. As noted previously, the R&D firms can. price their ideas exactly to extract all the profit of the intermediate firms.. For this. reason, a higher θ (as well as the profit of the intermediate firms) means that more resources are contributed to hire labor in the R&D sector, thereby stimulating the balanced growth rate. In the GA regime, on the contrary, the effects of θ on long-term growth rate 24.

(30) and welfare are negative but almost negligible.. The reason for this result stems from. the fact that in the GA regime abatement investment is undertaken only by the government, and thus has no direct relationship with the firms’ profit.. More. specifically, the numerical simulations depicted in Figure 2.1 indicate that, under both the PA and PAR regimes, the greater the degree of imperfect competition, the larger the benefit of private abatement will become.. When θ is large enough, both the. balanced growth rate and social welfare for the PA regime may possibly exceed those for the GA regime.. Moreover, if the government can recycle its tax revenues to. provide incentives for private abatement R&D, both economic growth and welfare will be further enhanced. 2.4.2.2. The type of government spending We now discuss the parameter related to the public sector.. In their recent study,. Fullerton and Kim (2008) show that government spending on transfer payments (φ ) is a non-environmental parameter with important implications for environmental policy. The effect of changing φ is depicted in Figure 2.2.. It is quite clear that, in response. to an increase in φ , the growth rate and social welfare decline in both the PAR and GA regimes but remain intact in the PA regime. The intuition for this result is straightforward.. In the PA regime all tax revenues are returned to the households.. The abatement investment which stirs up economic growth comes only from the monopolistic rents so that φ has no role in economic activities. However, under both the PAR and GA regimes, economic growth becomes closely related to φ since the government uses its tax revenues to stimulate (or directly conduct) abatement R&D.. A positive value of φ indicates that part of the. revenues from the environmental tax must be spent on transfer payments.. The. greater need for transfer payments implies that less tax revenue will be used in. 25.

(31) abatement R&D, and hence will lead to deterioration in the balanced growth rate. As is evident, our results indicate that the Fullerton and Kim (2008) conclusion is valid under both the PAR and GA regimes and invalid under the PA regime. 2.4.2.3. The effect of an environmental tax We now turn to investigate the effect of environmental tax policy.. It is shown. in Figure 2.3 that raising an environmental tax can stimulate economic growth as well as reduce the level of pollution.. Bovenberg and Smulders (1995) have clearly. pointed out the two opposing forces whereby the environmental policy affects the long-term growth rate.. First, a lower level of polluting inputs decreases the. productivity of reproducible inputs, thereby lowering economic growth.. Second, a. reduction in pollution improves the environmental quality, which benefits productivity and economic growth.. As a result, Bovenberg and Smulders (1995) suggest that. there is the environmental tax has an ambiguous effect on economic growth. In our model, however, by referring to (2.6), the pollution inputs are purchased from abroad at a given price so that a higher environmental tax can simultaneously reduce the pollution p (= pi ) but keep the polluting inputs e (= ei ) unchanged. Under such a situation, a tighter environmental policy no longer decreases the productivity of capital and labor, because a lower level of pollution in production is offset by more abatement knowledge.. Hence, our model only presents the second. environmental quality effect. To highlight the importance of this environmental quality effect, we consider the alternative value γ = 0 to show that production gains no extra benefit from a better environmental quality.. The simulation results are depicted in Figure 2.4.. It can be. seen that, in the absence of an environmental externality, raising an environmental tax has no effect on the long-term growth rate while it reduces pollution. Comparing. 26.

(32) Figure 2.3 with Figure 2.4 enables us to realize that whether or not environmental policies affect economic growth crucially depends on the presence of a positive environmental externality. In our model, as mentioned above, a fixed import price of polluting inputs ( m ) is the key to screening out the traditional negative policy effect on long-term growth in the literature.. Therefore, it is worthwhile discussing why we need to introduce this. parameter into our model.. Theoretically, although numerous studies model pollution. based on the concept of a “dirty input”, there are several reasons for treating them differently.14. First, pollution (i.e., dirty air, messy water or noise) is not directly used. in the production process, while the dirty inputs (i.e., petroleum or chemicals) are. Second, abatement knowledge can hardly play any role in the pollution transformation process if we mix the two.. Third and most importantly, pollution harms human. health but is not internalized by the private agents and thus needs to be priced by the government, while dirty inputs should be priced by the market, because they are production factors just like other clean inputs.. Hence, we allow for τ P and m to. denote, respectively, the price of pollution and dirty inputs. To be more specific, suppose that there is no polluting input price, from (2.5)-(2.7) and q = 1 (the zero-profit condition in the final good sector) we have: α. π i = A( N )ki pi. ε (1−α ). β. H 1−α l yi − rki − ω l yi − τ P pi .. (2.39). One implication stemming from (2.39) is that, in the absence of any policy interference ( τ P = 0 ), the cost of pollution becomes zero so that the intermediate firms will select an infinitely large level of pollution.. As a result, the environmental. quality declines to the bottom and the economy cannot survive even temporarily. 14. To. Some studies (e.g., Ligthart and van der Ploeg, 1994; Smulders and Gradus, 1996; and Bréchet and Michel, 2007), on the other hand, treat pollution as a by-product of capital or final output. However, under such a situation, since an environmental tax levied on pollution is equivalent to that levied on physical capital or output, it might be difficult to tell whether economic growth is affected by an environmental tax or by a similar capital (output) tax. 27.

(33) this end, we introduce such a “non-policy” cost of polluting inputs to restrict the pollution to within a finite level even in the absence of an environmental tax.. To be. concerned with practicality, since firms usually import petroleum from abroad at a price that they can not bargain for, we believe that the assumption of a given price of polluting inputs is not very far from the real world. Now we turn to welfare considerations.. Figure 2.3 and Figure 2.4 show that the. welfare level is increasing with the environmental tax, regardless of whether a positive environmental externality is present or not.. As discussed earlier, in the case. of γ = 0 a tighter environmental policy has no effect on long-term growth. However, it can still influence the level of welfare.. More specifically, with the. growth rate unchanged, a higher environmental tax reduces pollution to improve the environmental quality, and thus unambiguously enhances the welfare level.. If the. representative household does not care about the environmental quality ( η = 0 ), it is our conjecture that environmental policy cannot play any role in governing the balanced growth rate and the welfare level.. 2.5. Concluding Remarks This chapter develops an endogenous growth model featuring an environmental externality, abatement R&D, and market imperfections.. The salient trait of the. model is that it is able to deal with three distinct regimes including public abatement, private abatement without tax recycling, and private abatement with tax recycling. Some main findings are obtained from our simulation analysis.. First, there exists a. trade-off between economic growth and environmental quality in a “regime selection” sense. Second, the benefit arising from the private conduct of abatement becomes larger the greater the degree of the firms’ monopoly power.. This potentially implies. that antitrust policies might in some way reduce growth and welfare in a private 28.

(34) abatement R&D model.. Third, if the government recycles the environmental tax. revenues to subsidize private abatement R&D, the growth rate and welfare will almost be higher than those in any other regimes.. Fourth, the beneficial effects of public. abatement policies will be eroded when government spending on transfer payments increases. The effects of environmental tax policies are also investigatedr.. We show that a. rise in the environmental tax could possibly simultaneously reduce pollution and stimulate growth if the intermediate firms import polluting inputs from abroad at a fixed price.. However, care should be taken regarding the implications because such. a desirable result is in part due to the rigidity of the polluting input price.. If the. import price can be adjusted endogenously, the above result should be modified as well. Although our model indicates that an environmental tax policy is beneficial to economic growth, we would like to mention that this result should be accepted with some caution.. In fact, our main intention is not to emphasize the beneficial effect of. an environmental tax on economic growth, but to highlight the importance of distinct pricing between pollution and polluting inputs.. Doing so will be helpful for us to. clarify the two channels through which an environmental tax influences the long-term growth rate, i.e., the (negative) traditional productivity effect and the (positive) Bovenberg-Smulders environmental quality effect. Some extensions could be considered in future research.. First, R&D firms can. extract all their buyers’ profit via their unilateral determination of the license fee.. It. would be interesting to consider the case where the license fee for abatement knowledge is decided by a Nash-bargaining process between R&D firms and intermediate firms instead of by R&D firms only. inputs is not internalized in this analysis. 29. Second, the price of polluting. It is natural to extend our model by.

(35) proposing a channel to endogenize the polluting input price.. For instance, we can. introduce an additional domestic energy sector, or assume a nonlinear adjustment cost of polluting inputs.. These extensions inevitably complicate the model, but they. deserve future study.. 30.

(36) Appendix This appendix provides a detailed derivation of (2.34) and (2.36) in the main text. In the PA regime, by substituting the intermediate firm’s first-order conditions reported in (2.10)-(2.12) into the profit function, we obtain:. π = [1 − (1 − θ )(α + β ) − (1 − θ )(1 − α )ε ]Y − (1 − ε )mHP ε . Based on g = H / H and (2.29), we have H / H = π / q H H .. (A2.1). Then, putting (2.12),. (2.17), and (2.20) and H / H = π / q H H together, we can derive: g=. H δπ = . H ω. (A2.2). Substituting (A2.1) into (A2.2) yields:. g=. δ [1 − (1 − θ )(α + β ) − (1 − θ )(1 − α )ε ] δ (1 − ε )mHP ε Ly − . ω (1 − θ ) β. (A2.3). By substituting the relevant variables along the balanced growth equilibrium into (A2.3) and reminding h = H / K and w = ω / K , we can obtain (2.34) in the main text. In the PAR regime, from (2.17), (2.30) and (2.31) we have g = δπ /(1 − s )ω . Similar to the derivation of (2.34) in the PA regime, we can obtain (2.36) in the main text.. 31.

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(40) Figure 2.1. The effect of monopoly power. PAR:. GA:. PA:. 0.05. growth rate. 0.04 0.03 0.02 0.01 0.00 0.30. 0.31. 0.32. 0.33. 0.34. 0.35. 0.36. 0.34. 0.35. 0.36. monopoly power. -20. Welfare. -40. -60. -80. -100. 0.30. 0.31. 0.32. 0.33 monopoly power. 35.

(41) Figure 2.2. The effect of increasing other government spending. 36.

(42) Figure 2.3. The effect of an environmental tax ( γ = 0.77 ). PAR:. GA:. PA:. 0.0025 0.032 -48. 0.030. 0.028. 0.0015. welfare. pollution. growth rate. 0.0020. 0.0010. -50. -52. 0.0005 0.026. -54. 0.0000 20. 40. 60. 80. 20. 100. 40. 60. 100. 20. 40. 60. pollution. 0.0170. 80. 100. 80. 100. environmrntal tax. 0.0020. -66. 0.0015. -67. welfare. 0.0175. growth rate. 80. environmrntal tax. environmrntal tax. 0.0010. -68. 0.0165 -69. 0.0005. 0.0160. 0.0000 20. 40. 60. 80. 100. -70. 20. 40. environmrntal tax. 80. 100. 20. 40. environmrntal tax. 60 environmrntal tax. 0.0030. 0.045. pollution. 0.044 0.043. 0.0025. -36. 0.0020. -38. welfare. 0.046. growth rate. 60. 0.0015. 0.042. 0.0010. 0.041. 0.0005. -40 -42 -44. 0.040. 0.0000. 20. 40. 60 environmrntal tax. 80. 100. 20. 40. 60. 80. environmrntal tax. 37. 100. 20. 40. 60 environmrntal tax. 80. 100.

(43) Figure 2.4. The effect of an environmental tax ( γ = 0 ). PAR:. GA:. PA:. 0.035. -46. 0.0025. 0.034. -48. 0.032. welfare. 0.033. pollution. growth rate. 0.0020 0.0015 0.0010. 0.031. 0.0005. 0.030. 0.0000. -50. -52. -54. 20. 40. 60. 80. 100. 20. 40. environmrntal tax. 60. 80. 20. 100. 40. 60. 80. 100. 80. 100. environmrntal tax. environmrntal tax. 0.0180 0.0020. -66. 0.0015. -67. 0.0174. 0.0010. 0.0000 20. 40. 60. 80. -68. -69. 0.0005. 0.0172. 0.0170. welfare. 0.0176. pollution. growth rate. 0.0178. -70. 100. 20. 40. environmrntal tax. 60. 80. 100. 20. 40. 60. environmrntal tax. environmrntal tax. 0.050. -34. 0.0030. 0.044. 0.042. -36. 0.0020. welfare. 0.046. 0.040. -35. 0.0025. pollution. growth rate. 0.048. 0.0015 0.0010. -38. 0.0005. -39. 0.0000. 20. 40. 60 environmrntal tax. 80. 100. -37. -40. 20. 40. 60. 80. environmrntal tax. 38. 100. 20. 40. 60 environmrntal tax. 80. 100.

(44) Chapter III ___________________________________________________________. Intergenerational Welfare and Pareto-improving Environmental Policies 3.1. Introduction One important feature of environmental issues is that the degradation of the environment requires a period of time.. The existing generations who create. pollution today may not live long enough to bear the consequences of environmental deterioration in the future.. Environmental policies, therefore, should be responsible. for internalizing both intratemporal and intertemporal environmental externalities (Heijdra et al., 2006).. As heterogeneous generations are considered, the following. questions naturally arise: What is the environmental policy impact on the welfare of different generations?. Does an intergenerational welfare conflict emerge from. raising an environmental tax?. Is it possible for an environmental tax to be. Pareto-improving (i.e., to improve the welfare of all generations)?. This makes an. attempt to deal with these questions. To this end, we set up an overlapping generations (OLG) growth model building on the work proposed by Samuelson (1958) and Diamond (1965), and use it to examine the welfare effects of an environmental tax on different generations. on this OLG growth model, several main results emerge from our analysis.. Based. First, the. pattern whereby tax revenues are distributed to either the young generation or the elderly generation plays an important role in determining intergenerational welfare and economic growth.. Second, the growth effect of environmental policies is. governed by evaluating the welfare changes of the generations born in the endless future.. Third, the diverse environmental policy effects may emerge from the. 39.

(45) environmental utility of the existing generations. Finally, we show that a. Pareto-improving environmental policy is achievable in the presence of positive environmental production externalities. Two studies closely related to the present chapter are Bovenberg and Heijdra (1998) and Heijdra et al. (2006), who build on the OLG model proposed by Yaari (1965) and Blanchard (1985) and study the intergenerational welfare effect of an environmental tax.. It is therefore worthwhile discussing the major differences. between our analysis and theirs.. First, they show that, in response to a rise in the. environmental tax rate, the returns of productive factors decline so that the existing older generations who have accumulated a huge amount of physical capital must. accordingly suffer from an immense non-environmental loss.. The newborn. generations, on the contrary, have not yet accumulated wealth and thus enjoy a welfare gain from the distributed tax revenues.. This result is the basic spirit of the. Yaari-Blanchard OLG model in that the older generations are inevitably the richer generations (by accumulating more wealth). Based on this feature, in their analysis the environmental tax is essentially more harmful to the richer generations than to the older generations.. To escape from such a rigid and somewhat unrealistic. intergenerational linkage, in the present. we instead use the Samuelson-Diamond. OLG model to deal with the intergenerational welfare distribution effect of the environmental tax. Second, the Yaari-Blanchard OLG model assumes that all existing generations face the same mortality and thus expect the same remaining life time (the so-called “perpetually youth” assumption).. Based on this distinctive trait, as the. environmental tax rises, the changes in the environmental utility of all existing generations － no matter how old or young, are entirely equivalent.. In reality,. however, the existing old generation who may have no further remaining life time can 40.

(46) hardly wait for the reaping of environmental fruits.. From this perspective, raising. the environmental tax should affect only the (environmental) welfare of the existing young generation rather than of all existing generations.. While the Yaari-Blanchard. OLG model can not reflect such an intergenerational welfare contradiction, our analysis can escape from this drawback and provide an insight for this issue. Moreover, in Bovenberg and Heijdra (1998) and Heijdra et al. (2006) featured with Yaari-Blanchard OLG, the asset stock of the older generations is greater than that of the younger generations.. Then, in response to a rise in the environmental tax rate,. the older generations must bear a higher part of the environmental tax burden and their welfare level is certainly lowered.. Their result essentially stands in line with. John and Pecchenino (1994), who argue that with no private maintenance investment, an environmental policy can hardly be Pareto-improving.15. Our analysis instead. possesses an advantage in that it assigns a specific proportion of government transfers to each generation.. In particular, we introduce the positive environmental externality. in production, and hence are able to show that, even in a quite reasonable way to distribute the tax revenues, an environmental tax could be Pareto-improving. This chapter is also related to the strand of the literature on the linkage between environmental policies and endogenous economic growth.. Most of these studies. confine their analysis to the model with the infinitely-lived household (e.g., Bovenberg and Smulders (1995), Mohtadi (1996), Smulders and Gradus (1996), Byrne (1997), Bovenberg and de Mooij (1997), Stokey (1998), Grimaud (1999), Nakada (2004), Itaya (2008), Fullerton and Kim (2008)).16. Others deal with an OLG. model either based on the Yaari-Blanchard framework (Pautrel, 2008; 2009) or on the 15. However, Bovenberg and Heijdra (1998) demonstrate that if the government can implement an intergenerational redistribution policy (public debt) to allow the future generations who enjoy most of the environmental gain to compensate the existing generations, then it is possible for all generations to benefit from the environmental tax. 16 See Xepapadeas (2005) for a survey of this literature. 41.