1. Introduction
The relationship between economic growth and environmental pollution is one of the most concerning topics among environmental economists. Many of the debates centered on the proposition of the Environmental Kuznets Curve (EKC), which was formulated by Grossman and Krueger (Reference Grossman and Krueger1991) and Panayotou et al. (Reference Panayotou1993). The EKC argues that there is an inverted U-shape between economic growth and environmental pollution: pollution first increases as the economy flourishes and then decreases after a turning point as the economy grows. The EKC posits a notion that economic growth can naturally lead to a comeback of clean environment. As Beckerman (Reference Beckerman1992) argues, “there is clear evidence that, although economic growth usually leads to environmental degradation in the early stages of the process, in the end the best and probably the only way to attain a decent environment in most countries is to become rich.” (P. 491).
Following this tenet, in practice, may be harmful. Stern (Reference Stern2017) concerns that “the EKC literature might encourage policymakers to incorrectly de-emphasize environmental policy and pursue growth as a solution instead.” (P. 24). It supports a strategy of “pollute first, remediate later,” with a belief that a region could achieve economic growth by sacrificing the environment, and once people become wealthy, they will have stronger willingness, larger financial capacity, and better technologies for environmental protection, from which a clean environment will naturally ensue. For instance, the two cities in China, Wenchuan and Beichuan, which collapsed into rubble in the 2008 earthquake, decided to rebirth as ecological cities but eventually turned instead to pollution-intensive industries, in an effort for economic recovery. However, it is questionable whether this development model could eventually lead to a comeback of clean environment and simultaneously sustainable economic growth.
Theoretically, the EKC argument has two implicit assumptions. First, it assumes a unidirectional relationship from economic growth to pollution and implicitly ignores the reverse impact of pollution on economic growth. As Stern (Reference Stern2004) writes, “the EKC model,
$\ldots$
, assumes that there is no feedback from environmental damage to economic production as income is assumed to be an exogenous variable.” (P. 1426). However, a large body of literature shows that environmental degradation negatively affects working productivity (e.g., Zivin and Neidell, Reference Zivin and Neidell2012; Chang et al. Reference Chang, Zivin, Gross and Neidell2016; Fu et al., Reference Fu, Viard and Zhang2021). In particular, several lines of literature show that human capital are evidently impaired by pollution. Cavalcanti et al. (Reference Cavalcanti, Mohaddes, Nian and Yin2023) show that air pollution significantly reduces human capital’s creativity, and the negative effects are more salient among human capital who works on high-quality innovations. Another branch of literature shows that pollution decreases human’s cognitive development, such as school performance and education years (e.g., Currie et al. Reference Currie, Hanushek, Kahn, Neidell and Rivkin2009; Ebenstein et al. Reference Ebenstein, Lavy and Roth2016; Bharadwaj et al. Reference Bharadwaj, Gibson, Zivin and Neilson2017; Zivin et al. Reference Zivin, Liu, Song, Tang and Zhang2020). The development of pollution-intensive industries creates an environment unsuitable for people to advance their own and children’s education. Moreover, human capital is less likely to resident in polluting areas than labor. Hart (Reference Hart2020) shows that high-skilled workers have stronger preference over environmental amenities. The flexible job choices and income enable them to migrate more freely than low-skilled labor. In addition, while human capital basically works indoor, Archsmith et al. (Reference Archsmith, Heyes and Saberian2018) show that the variation in outdoor pollution exerts negative effects on the indoor activities as well. Taking the feedback effects of pollution on human capital into account, the model shows that the development of pollution-intensive industries impairs a region’s capability for long-run economic growth, although it helps gear up a short-run prosperity. Second, the EKC assumes that environmental damage is reversible at a reasonable cost. This might be true for some types of pollution but not for many others, such as soil contamination, desertification, and loss of biodiversity (Arrow et al. Reference Arrow, Bolin, Costanza, Dasgupta, Folke, Holling, Jansson, Levin, Mäler, Perrings and Pimentel1995), the remediation of which is prohibitively expensive. The ongoing concern over climate change is one example, and the long-standing brownfield dilemma for urban redevelopment in the USA is another example (High, Reference High2017).
When pollution is very difficult to remediate and the feedback impact of pollution on economic growth is significant, it is likely that a region that initially relies on dirty technology would be trapped in a low development level instead of following the EKC pattern. This study is to theorize the feedback mechanism and constrained pollution reversibility into an endogenous growth model. We start with an endogenous growth model to describe a clean economy, in which human capital accumulation serves as the engine for growth. We then extend the model to capture a dirty economy, in which pollution emitted by manufacturing sector is considered as a stock variable and exerts external costs on knowledge-producing activity by reducing the efficiency of education and research sector. As a result, the dirty economy loses its growth engine because the stock of pollution crowds out labor allocation to the education and research sector and reduces the efficiency of human capital accumulation. Provided with an exogenous choice between a clean versus a dirty technology, the model shows how social welfare, physical capital, human capital, pollution, and abatement are endogenously determined in equilibrium and dynamically evolve over the short and the long run.
We find that the dirty economy experiences temporary prosperity by sacrificing the environment in the early stage but stagnates at a low-level equilibrium in the long run, whereas the clean economy is capable of sustainable growth. Even in a social optimal system that can fully internalize externalities, the dirty economy still ends up with a growth trap because of the pollution-induced losses of human capital accumulation. Within this framework, we also discuss the cost that a region will have to pay if it later decides to “remediate and switch” to a clean path of development. The pain for this switch depends not only on the search friction and financial friction in the reallocation of used capital and labor (Dong et al., Reference Dong, Wang and Wen2020; Dong, Reference Dong2022) but also on the friction of transitioning resources (capital, labor, and human capital) across occupations (Kambourov and Manovskii, Reference Kambourov and Manovskii2009)—from polluting industries into clean industries, as well as on the reversibility of environmental degradation. At last, we discuss policies including pollution tax and human capital subsidies. We observe a trade-off between the short-run and the long-run development in the choice of tax and subsidy rates. A higher taxation rate leads to less pollution and slows down the economy in the short run, but it contributes to a higher development level in the long run. This is close in spirit to the study by He et al. (Reference He, Huang and Ning2021) who highlight the positive relationship between taxation and the future accumulation of health capital. The difference between us exits in divergent mechanisms: He et al. (Reference He, Huang and Ning2021) suggest that high taxation on income leads to more leisure time and thus enhances human’s health and utility, while we emphasize the effects of taxation on curbing pollution, which reduces the harm on the efficiency of human capital accumulation and thus the long-run growth.
This paper contributes to three streams of literature. The first is built upon the vast literature on the EKC hypothesis, with an attempt to enhance our understanding with regard to the interaction between economic growth and environmental degradation. After Grossman and Krueger (Reference Grossman and Krueger1991) and Panayotou et al. (Reference Panayotou1993), significant efforts have been made to provide a theoretical underpining for the EKC pattern (Stokey, Reference Stokey1998; Andreoni and Levinson, Reference Andreoni and Levinson2001; Smulders, Reference Smulders2006; Brock and Taylor, Reference Brock and Taylor2010; Figueroa and Pasten, Reference Figueroa and Pasten2015; Hart, Reference Hart2020). They argue that the scale effect dominates when people are poor, whereas the technique effect dominates when people become rich. Then, the increasing willingness to pay (WTP) for clean environment makes the implementation of expensive clean technology feasible. However, far too little attention has been paid to the feedback mechanism—pollution stock negatively affects human capital accumulation by weakening human’s health and the efficiency in the education and research sector. A theoretical work that highlights this mechanism in an endogenous growth model is undertaken by Bosi and Ragot (Reference Bosi and Ragot2013). A large and growing body of literature has shown empirical evidence on this feedback mechanism, but the theoretical discussions on this topic is far from sufficient.
The EKC hypothesis also inspires many economists to empirically examine the relationship between economic growth and pollution. Different measurements of environmental degradation are used, and different countries and regions are investigated (e.g., Ahmad et al. Reference Ahmad, Zhao, Shahbaz, Bano, Zhang, Wang and Liu2016; Esteve and Tamarit, Reference Esteve and Tamarit2012; Fodha and Zaghdoud, Reference Fodha and Zaghdoud2010; Jalil and Mahmud, Reference Jalil and Mahmud2009; Holtz-Eakin and Selden, Reference Holtz-Eakin and Selden1995). The best takeaway from this vast empirical literature seems to be a doubt of the existence of a simple and predictable relationship between pollution and income (Copeland and Taylor, Reference Copeland and Taylor2004; Stern, Reference Stern2004; Stern, Reference Stern2017). These empirical endeavors are generally based on reduced-form regressions. The empirical setup is consistent with the EKC and implicitly assumes that pollution is a function of economic growth, without a feedback reversely from pollution to economic growth. In reality, however, the economy always interacts with the environment in a complex and dynamic manner, which cannot be precisely described by a static reduced-form model. As a modest effort to fill this gap, this paper provides a structural model to explore the dynamic interaction between the environment and the economic growth.
Second, this paper contributes to the understanding of the interactions among the environment, human capital, and economic growth in a macroeconomic framework. Our model is based on the endogenous growth theory pioneered by Lucas (Reference Lucas1988), Romer (Reference Romer1986, Reference Romer1990), and Rebelo (Reference Rebelo1991), in which knowledge and human capital accumulation serve as drivers of growth. The endogenous growth model has been exploited extensively in discussing environment and growth issues (Ligthart and van der Ploeg, Reference Ligthart and van der Ploeg1994; Bovenberg and Smulders, Reference Bovenberg and Smulders1995; Byrne, Reference Byrne1997; Stokey, Reference Stokey1998; Goulder and Mathai, Reference Goulder and Mathai2000). Different from previous studies, in this paper, pollution is a stock variable and exerts external costs on education and research sector. As such, we made the feedback mechanism clear in our model—pollution negatively affects long-run economic growth though the damages on human capital accumulation, a step forward from earlier dynamic models (Brock and Taylor, Reference Brock and Taylor2010; Criado et al., Reference Criado, Valente and Stengos2011; Bosi and Ragot, Reference Bosi and Ragot2013; Lopez and Yoon, Reference Lopez and Yoon2014). In this paper, we present a different pattern in which the dirty economy experiences temporary prosperity in the early stage but gradually loses its engine for growth and stagnates at a low-level equilibrium because of inadequate human capital accumulation.
Third, our model characterizes another element that is often ignored by the EKC literature, that is, the irreversibility of environmental degradation. Stokey (Reference Stokey1998) theoretically explores the cumulative effects of past pollution, but she assumes that environmental damage is self-correcting and has no effect on production activities, by which the EKC curve ensures. Nevertheless, the reversibility varies with the type of pollution. Some types of pollution, such as sulfur dioxide (
$\textsf{SO}_2$
) in the air and
$\textsf{COD}$
in the water, might be naturally removed, but some are prohibitively expensive to remove, such as soil contamination, climate change, and loss of biodiversity, many of which would become a permanent constraint for long-run development.
Last but not least, we compare the dirty and clean paths of development in a decentralized system with those in a social optimal system as benchmark. An important departure from previous work is that we emphasize both the short-run and the long-run dynamics. Previous studies place more emphasis on the long-run equilibrium, for example, balance growth rate or steady state (Gradus and Smulders, Reference Gradus and Smulders1993; Bovenberg and Smulders, Reference Bovenberg and Smulders1995; Byrne, Reference Byrne1997), except that Klarl (Reference Klarl2016) places more weight on the transition dynamics relative to the equilibrium behavior in policy design. In this paper, we also particularly discuss more on the short-run transition dynamics because it links to officials’ incentives for career promotions, a reason why the dirty technology is often initially chosen.
The rest of the paper proceeds as follows. Section 2 presents the model. Section 3 calibrates the structural parameters. Section 4 simulates the model and conducts a quantitative analysis on the transition dynamics and equilibria. Section 5 discusses policy interventions. Section 6 provides a further discussion. Section 7 concludes the paper.
2. Model
This section presents a dynamic model to highlight that an economy loses its engine for long-run economic growth through the mechanism of pollution-induced inefficiency of human capital accumulation. Here, human capital represents educated or trained employees or knowledge itself. We extend a standard endogenous growth model in the following manners: pollution from manufacturing sector accumulates over time; and it exerts external costs on knowledge-producing activities by reducing the productivity of the education and research sector.
2.1. Decentralized dirty economy
Time is infinite and discrete, indexed by
$t=0,1,\cdots$
. The economy is inhabited by a continuum of households, who consume goods, supply labor, and accumulate physical capital and human capital; a continuum of firms that produce consumption goods and emit pollution; and a continuum of education and research institutions that produce human capital. All the markets are competitive.
2.1.1. Household
A representative household consists of a continuum of agents, each of whom can be employed either in the manufacturing sector or the education and research sector. Total labor provided by the household is given by
$L=l_{yt}+l_{ht}$
, where
$l_{yt}$
and
$l_{ht}$
stand for the labor allocated to manufacturing sector and education and research sector, respectively. The household accumulates both physical capital
$k_{t}$
and human capital
$h_{t}$
.
Income can be used on a one-to-one basis for consumption
$c_t$
and physical capital accumulation; it can also be used on human capital accumulation, which is priced at
$p_{ht}$
, measured by consumption goods. In the polluting economy, pollution
$x_t$
causes disutility to the household. By choosing consumption, capital, and human capital, the household maximizes its expected present value of utility over an infinite horizon:
\begin{equation*}\max _{\{c_t,k_{t+1},h_{t+1}\}}\sum _{t=0}^\infty \rho ^t\Big (\frac {c_t^{1-\sigma }-1}{1-\sigma }-\frac {Dx_t^\gamma }{\gamma }\Big ), \end{equation*}
subjects to the budget constraint:
\begin{equation} c_{t} + k_{t + 1} - \left ({1 - \delta _{k}} \right )k_{t} + p_{ht}\left \lbrack{h_{t + 1} - \left ({1 - \delta _{h}} \right ) h_{t}} \right \rbrack = r_{t}k_{t} + w_{yt}(l_{yt} + l_{ht}) + w_{ht}h_{t} + \pi _{yt} + \pi _{ht} + T_t, \end{equation}
where
$\rho \in (0,1)$
is the discount rate for the future,
$\sigma \gt 0$
is the relative risk aversion parameter,
$D\gt 0$
is an exogenous parameter that describes the magnitude of the disutility, and
$\gamma \gt 1$
is the elasticity parameter in the disutility function of pollution. The left-hand side of equation (1) represents household’s spending on consumption and investments in physical capital and human capital, and the right-hand side represents household’s disposable income;
$w_{yt}$
,
$w_{ht}$
, and
$r_{t}$
represent labor wage, human capital wage, and capital rent, respectively. Total income also includes firm profits
$\pi _{yt}$
, institutional profits
$\pi _{ht}$
, and a lump-sum rebate
$T$
from tax on industrial pollution. Denoting
$\lambda _t$
as the Lagrangian multipliers of the budget constraint, the optimal conditions for
$\{c_t,k_{t+1},h_{t+1}\}$
are given by:
\begin{equation} c_{t}^{- \sigma } = \lambda _{t}, \end{equation}
\begin{equation} \lambda _{t} = \rho \lambda _{t + 1}\left ({r_{t + 1} + 1 - \delta _{k}} \right ), \end{equation}
\begin{equation} p_{ht}\lambda _{t} = \rho \lambda _{t + 1}\left \lbrack{w_{ht + 1}+p_{ht + 1}\left ({1 - \delta _{h}} \right ) } \right \rbrack. \end{equation}
Equation (2) is the optimal condition for consumption. Equations (3) and (4) are Euler equations for the optimal intertemporal decisions on physical capital and human capital, respectively.
2.1.2. Firm
In each period, output
$y_t$
is produced by combining physical capital, human capital, and labor. The production function takes the Cobb–Douglas form,
$y_{t} ={A_{d}k}_{t}^{\alpha }h_{t}^{1 - \alpha }{l_{yt}}^{1 - \alpha }\left ( 1 - z_{t} \right )$
, and
$0 \lt \alpha \lt 1$
.
$A_d$
is the technical parameter in the dirty economy and remains time-invariant.
$z_{t} \in \left \lbrack 0,1 \right \rbrack$
denotes the level of pollution abatement. A lower value of
$z_t$
yields more outputs but more pollution.
$z_t=0$
corresponds to the potential output in the most polluting way. The production function exhibits neoclassical properties: positive and diminishing marginal products of each input and satisfies the Inada conditions.
In reality, environmental pollution accumulates over time and has cumulative effects on future economic activities. To capture this fact, we assume that pollution
$x_t$
is a stock variable,
$x_{t + 1} = \left ( 1 - \eta \right )x_{t}+ \left ( 1 - z_{t} \right )^{\beta -1}y_t$
, where
$\eta$
denotes the nature’s self-correcting capacity (Stokey, Reference Stokey1998) and
$\beta \gt 1$
. The second term
$\left ( 1 - z_{t} \right )^{\beta -1}y_t$
reflects the newly emitted pollution which increases with the output and decreases with the abatement
$z_t$
. The government controls pollution by taxing firms’ newly emitted pollution at the rate of
$\phi$
. We assume
$\phi \in \left \lbrack 0, + \infty \right )$
, implying that the government can stop production if the society’s WTP for the environment runs to infinity.
Since there is a continuum of firms in the manufacturing sector, in the decentralized economy, each firm is small and does not take pollution externalities into account when making production decisions. In each period, a representative firm chooses
$k_t$
,
$l_{yt}$
,
$h_t$
, and
$z_t$
to maximize its profit:
\begin{equation*} \pi _{yt} = \underset {\{{k_{t},l_{yt},h_{t},z_t}\}}{\max }{A_{d}k}_{t}^{\alpha }h_{t}^{1 - \alpha }{l_{yt}}^{1 - \alpha }\left ( {1 - z_{t}} \right ) - r_{t}k_{t} - w_{yt}l_{yt} - w_{ht}h_{t} - \phi A_{d}{k_{t}}^{\alpha }{l_{yt}}^{1 - \alpha }{h_{t}}^{1 - \alpha }\left ( {1 - z_{t}} \right )^{\beta }. \end{equation*}
The optimal conditions with respect to
$k_t$
,
$l_{yt}$
,
$h_t$
, and
$z_t$
are given by:
\begin{equation} r_{t} =\alpha{A_{d}k}_{t}^{\alpha -1}\left ( h_{t}{l_{yt}}\right ) ^{1-\alpha }(1-z_{t})\left [ 1-\phi \left ({1-z_{t}}\right ) ^{\beta -1}\right ], \end{equation}
\begin{equation} w_{yt} ={\left ({1-\alpha }\right ) A_{d}k}_{t}^{\alpha }h_{t}^{1-\alpha }{l_{yt}}^{-\alpha }(1-z_{t})\left [ 1-\phi \left ({1-z_{t}}\right ) ^{\beta -1}\right ], \end{equation}
\begin{equation} w_{ht} ={\left ({1-\alpha }\right ) }A_{d}{k}_{t}^{\alpha }h_{t}^{-\alpha }{l_{yt}}^{1-\alpha }(1-z_{t})\left [ 1-\phi \left ({1-z_{t}}\right ) ^{\beta -1}\right ], \end{equation}
\begin{equation} \phi \beta = \left ({1-z_{t}}\right ) ^{1-\beta }. \end{equation}
In this setting, the firm’s problem does not involve intertemporal elements, and hence it maximizes static profit in each specific period. Equations (5), (6), and (7) show that, for each input, its market price equals its marginal product. Taking the pollution tax rate as given, the firm chooses an optimal pollution abatement level according to condition (8).
2.1.3. Education and research sector
The education and research institution hires labor to cultivate human capital and produces knowledge. The process of human capital accumulation is given by:
\begin{equation} \Delta h_{i,t + 1} = Bl_{i,ht}\left ( 1 + x_{t} \right )^{- \xi }h_{t}, \end{equation}
where
$\xi \geq 1$
measures the extent to which pollution decreases the efficiency of human capital accumulation in light of the empirically plausible evidence.
$B$
denotes the technical parameter and remains time-invariant, and
$l_{i,ht}$
denotes the amount of labor working in each education and research institution
$i$
.Footnote
1
$\Delta h_{i,t + 1} = h_{i,t + 1} - \left ({1 - \delta _{h}} \right )h_{i,t}$
is the amount of human capital produced in period
$t$
.
$\delta _h$
is the depreciation rate of the stock of human capital. The newly produced human capital in the clean economy is
$\Delta h_{i,t + 1} = Bl_{i,ht}h_{t}$
.Footnote
2
An individual institution chooses the optimal level of
$l_{ht}$
to maximize profit:
\begin{equation*} \pi _{i,ht} = \max \limits _{\{ l_{\mathit {ht}}\}}p_{ht}B\left ( 1 + x_{t} \right )^{- \xi }l_{i,ht}h_{t} - w_{yt}l_{i,ht}. \end{equation*}
The optimal condition for
$l_{i,ht}$
is given by:
\begin{equation} p_{ht}B\left ({1 + x_{t}} \right )^{- \xi }h_{t} = w_{yt}. \end{equation}
The allocation of labor is determined by the non-arbitrage condition: working in the manufacturing sector and the education and research sector earns the same wage
$w_{yt}$
. The existence of pollution, however, discourages labor from working in the education and research sector because it decreases the marginal productivity of this sector. As a result, compared to the clean economy, a smaller proportion of labor will be devoted to the education and research sector; and human capital accumulation is relatively inadequate. This is more of a phenomenon as pollution accumulates and finally traps the economy in a slump where growth loses its internal engine–human capital accumulation.
In equation (9), there are three mechanisms playing important roles. The first mechanism is driven by learning by doing effects. As Romer (Reference Romer1986) proposed, the productivity improvement of human capital accumulation comes from the accumulation itself. More specifically, an education and research institution can simultaneously produce human capital and learn how to produce more efficiently. The second mechanism is driven by spillover effects. As each institution
$i$
expands
$h_{i,t}$
,
$h_t$
rises accordingly and results in spillover effect that raises the productivity of the entire sector (Lucas, Reference Lucas1988). Nevertheless, since an individual institution is too small to consider its own contribution to the aggregate, in the decentralized economy, it takes
$h_t$
as given and fails to internalize the spillover effects. The third mechanism is driven by pollution externalities, because of which both learning by doing and spillover effects are largely muted over time, ruling out the possibility of endogenous economic growth.
2.1.4. Decentralized equilibrium
Throughout the paper, we define the balanced growth path (BGP) as a situation in which all the variables grow at a positive constant rate. If the growth rate is zero, we define it as steady state. Equations (1)–(10) define the full dynamics of the decentralized dirty economy. A decentralized general equilibrium consists of the steady-state consumption
$c^*$
, capital
$k^*$
, human capital
$h^*$
, output
$y^*$
, labor allocations
$\left \{{l_{h}^{*}, l_{y}^{*}} \right \}$
, pollution
$x^*$
, abatement
$z^*$
, and interest rate
$r^*$
such that:
$\left ( i \right )$
taking prices as given, allocations solve the maximization problem of each agent; and
$\left ( ii \right )$
the prices clear the markets for capital, human capital, labor, and final goods. Appendix A provides the description of the steady states.
2.1.5. Social optimal equilibrium
To offer insights for policy interventions, we discuss a social optimal equilibrium that the dirty economy can achieve. All the notations remain the same. A social planner maximizes social benefit:
\begin{equation*} \underset {\left \{ {c_{t},{l}_{ht},k_{t+1,}h_{t+1},x_{t+1}}\right \} }{\max }{\sum \limits _{t=0}^{\infty }{\rho ^{t}\left ( \frac {c_{t}^{1-\sigma }-1}{1-\sigma }-\frac {D{x_{t}}^{\gamma }}{\gamma }\right ) }}, \end{equation*}
subjects to the budget constraint:
\begin{equation} c_{t} + k_{t + 1} - \left ({1 - \delta _{k}} \right )k_{t} = A_{d}k_{t}^{\alpha }h_{t}^{1 - \alpha }{(1-l_{ht})}^{1 - \alpha }\left ({1 - z_{t}} \right ), \end{equation}
the law of motion of human capital accumulation:
\begin{equation} h_{t + 1} = Bl_{ht}{\left ({1 + x_{t}} \right )^{- \xi }h}_{t} + \left ({1 - \delta _{h}}\right )h_{t}, \end{equation}
and the law of motion of pollution accumulation:
\begin{equation} x_{t + 1} = \left ({1 - \eta }\right )x_{t}+{{A_{d}k}_{t}}^{\alpha }\left ({L - l_{ht}} \right )^{1 - \alpha }{h_{t}}^{1 - \alpha }\left ({1 - z_{t}} \right )^{\beta }. \end{equation}
Different from the agents in the decentralized economy, social planner can fully take the externalities of pollution from the manufacturing sector, as well as the spillover effects from the education and research sector into consideration. In particular, firms are required to abate pollution at the cost of production until the external costs on education and research sector are completely internalized. A social optimal equilibrium consists of the steady states of consumption
$c^*$
, capital
$k^*$
, human capital
$h^*$
, output
$y^*$
, labor allocations
$\left \{{l_{h}^{*}, l_{y}^{*}} \right \}$
, pollution
$x^*$
, and abatement
$z^*$
, such that allocations solve the social optimization problem. Appendix B provides the description of the steady states.
2.2. Decentralized clean economy
The clean economy is a special case of the dirty economy, in which pollution and its corresponding influences do not exit. Any divergence between the clean economy and the dirty economy can be interpreted as a consequence of pollution. For simplicity, we briefly present the general equilibrium put the description of agents’ problems in appendices.
2.2.1. Decentralized equilibrium
As we remove the law of motion of pollution accumulation, the externality of pollution no longer exists. The decentralized general equilibrium of a clean economy consists of the BGPs of consumption
$c_t$
, capital
$k_t$
, human capital
$h_t$
, output
$y_t$
, and labor allocations
$\left \{{l_{h}^{*}, l_{y}^{*}} \right \}$
, such that
$\left ( i \right )$
taking the prices as given, the allocations solve the optimization problem of each agent; and
$\left ( ii \right )$
the prices clear the markets for capital, human capital, labor, and final goods. The dynamic system is defined in Appendix C.
2.2.2. Social optimal equilibrium
In the social optimal clean economy, the first-best economic equilibrium is achieved with spillover effect internalized. This social optimal general equilibrium consists of the BGP of consumption
$c_t$
, capital
$k_t$
, human capital
$h_t$
, output
$y_t$
, and labor allocations
$\left \{{l_{h}^{*}, l_{y}^{*}} \right \}$
, such that the allocations solve the social optimization problem. The dynamic system is defined in Appendix D. In addition, since the clean economy exhibits endogenous growth properties and does not converge to steady states. We elaborate on how the clean economy finds an optimal way toward its BGP from an arbitrary starting point in Appendix E. In equilibrium, since labor allocations
$\left \{{l_{ht}, l_{yt}} \right \}$
, c-k ratio
$\frac{c_{t}}{k_{t}}$
, and k-h ratio
$\frac{k_{t}}{h_{t}}$
remain stable on the BGP, we can rearrange the model and construct a new dynamic system, through which, as long as the labor allocation, c-k ratio, and k-h ratio converge to their own steady states, the clean economy can reach its own BGP.
2.3. A summary of the model
In order to present a clear comparison, we summarize the characteristics of above four types of economic growth models in Table 1.
Table 1. A summary of the four types of economic development paths
The key insights are as follows. The social optimal clean economy achieves the first-best economic growth because the externalities are completely taken into account. The endogenous growth comes from the mechanisms of learning by doing (contributing to its own efficiency) and the internalized spillover effect (contributing to the efficiency of the entire education and research sector), which relaxes the constraint of diminishing returns to capital. The decentralized clean economy is also capable of endogenous growth, but to a smaller extent, because the spillover effect in the education and research sector is ignored in individual decisions. However, the social optimal dirty economy loses its engine for sustainable growth in that pollution from manufacturing sector exerts negative externalities on the productivity of the education and research sector. As a result, a larger proportion of labor will be allocated to manufacturing sector, which further weakens the learning by doing and spillover effects in the education and research sector. The decentralized dirty economy traps at a lower equilibrium than the social optimal dirty economy because individual agents neither internalize the pollution externalities from manufacturing sector nor the spillover effects from the education and research sector. Therefore, the economy loses its engine for endogenous growth, which implies that pollution is likely to rule out sustainable growth through the human capital channels.
3. Parameter calibration
We calibrate the model parameters based on China’s economy. The calibration is summarized in Table 2.
Table 2. Parameter calibration
3.1. Parameters in Human Capital Accumulation {
$\xi$
,
$B$
}
The critical parameter
$\xi$
represents the extent to which pollution diminishes human capital accumulation. The process of human capital accumulation can be rewritten as
$\frac{\Delta h_{t + 1}}{h_{t}} = B( 1 + x_{t})^{- \xi }l_{ht}$
, where
$\Delta h_{t + 1}$
represents the newly produced human capital and
$\frac{\Delta h_{t + 1}}{h_{t}}$
represents the average human capital productivity in the education and research sector. The parameter
$\xi$
is essentially an elasticity of the efficiency of human capital accumulation
$B(1+x_t)^{-\xi }$
on pollution.
In the empirical analysis, we adopt a linear econometric model to investigate the effects of pollution on human capital productivity. The specification is given by:
\begin{equation} \ln \textit{HumanCap}_{it} = \beta _{0} + \beta _{1}\ln \textit{Pollution}_{it} + \beta _{2}W_{it} + \mu _{i} + \phi _{t} + \sigma _{it}, \end{equation}
where
$i$
and
$t$
denote firm and year, respectively;
$\textit{HumanCap}_{it}$
represents human capital’s productivity, corresponding to the term
$B(1+x_t)^{-\xi }$
in our theory. We measure the human capital as employees who are engaged in knowledge-producing activities.
$X_{it}$
represents air pollution measured by
$PM_{2.5}$
.
$\beta _{1}$
is of our interest, and it represents how pollution affects human capital productivity. Error term (
$\varepsilon _{it}$
) absorbs the unobservable factors varying with year and firm-level characteristics. Firm fixed effect (
$\mu _i$
) is used to control for time-invariant firm-level characteristics. Year fixed effects (
$\phi _t$
) are included to control for macro shocks like national policies that affect human capital’s productivity.
$W_{it}$
denotes a vector of firm-level and meteorological control variables, including firm age and total assets, hours of sunlight, wind speed, and precipitation.
The dataset includes several sources: firm-level human capital and innovation information, county-level air pollution indicator
$PM_{2.5}$
, and county-level thermal inversion. The firm-level human capital data come from the Surveys of Science and Technology Activities of Industrial Firms (SSTA) database. The SSTA is conducted by China’s National Bureau of Statistics (NBS). Based on the SSTA database, human capital productivity is measured by total innovation per unit of human capital. Here, innovation is regarded as the outcome of human capital.Footnote
3
The publicly available data
$PM_{2.5}$
and thermal inversion are monitored by the Earth Observing System (EOS) of the National Aeronautics and Space Administration (NASA). We aggregate their annual average value from the grid to the county level.
The exposure to
$PM_{2.5}$
could be endogenous in different ways, such as unobserved social and political factors varying with time across regions. To address the potential endogeneity of pollution, we exploit a two-stage least squares (2SLS) approach by which we first use thermal inversion to instrument pollution (
$PM_{2.5}$
) and replace the independent variable in equation (14) with instrumented
$PM_{2.5}$
. Thermal inversion as a meteorological phenomenon is correlated with
$PM_{2.5}$
but uncorrelated with production activities. It occurs when the temperature at the upper atmospheric layer is higher than that of the lower layer, which prevents dissipating
$PM_{2.5}$
locally near the ground. The specification of first-stage estimation is defined as:
\begin{equation} \ln X_{it} = \alpha _{0} + \alpha _{1}\ln V_{it} + \alpha _{2}W_{it} + \tau _{i} + \theta _{t} + \epsilon _{it}, \end{equation}
where
$V_{it}$
denotes thermal inversion at firm
$i$
’s location in year
$t$
, respectively.
Table 3 reports the 2SLS results from the linear specifications in equations (14) and (15). Column (1) suggests that thermal inversion is a reliable predictor for
$PM_{2.5}$
. Column (2) shows that a 1% increase of
$PM_{2.5}$
significantly reduces human capital productivity by 0.149 innovation per capita. In calibration, we set the value of
$\xi =1.45$
by matching the simulated moments with the empirical facts in Table 3. Since choosing different measures of pollution (such as the mean or aggregate
$PM_{2.5}$
,
$PM_{10}$
) and thermal inversion (such as the frequency or the level at different atmospheric layers) might drive the estimate either upward or downward, we attempt to figure out how the economic pattern varies with
$\xi$
. Furthermore, we conduct a sensitivity analysis on parameter
$\xi$
. As shown in Figure F1, a larger value of
$\xi$
diminishes human capital accumulation to a larger extent. In the short run, the economic path is a bit higher than the baseline because the equilibrium condition of labor wage leads to a large proportion of labor flowing to final goods production. However, in the long run, less human capital accumulation leads to a significantly lower economic equilibrium than the baseline.
Table 3. Short-run effects of air pollution on human capital productivity (2SLS)
Notes: Human capital productivity is measured by total innovations divided by human capital stock. Firm controls include firm age and firm total assets, and weather controls include precipitation, temperature, and hours of sunlight. Standard errors are reported in parentheses. *** denotes significance at the 1% level.
We now discuss the calibration of parameter
$B$
. In our model,
$h_t$
represents the aggregate human capital in the education and research sector. It contributes to the productivity of each individual institution.
$B$
is the technical parameter representing the scale of spillover effects of
$h_t$
. It also contains the learning-by-doing effects of
$h_{i,t}$
: an individual institution can simultaneously produce human capital and learn how to produce efficiently. Nevertheless, we do not have access to reliable information about the technical parameter that represents both the spillover effects and learning-by-doing effects in the education and research sector in the background of China. In literature, Chyi et al. (Reference Chyi, Lai and Liu2012) use data from 92 Hsinchu Science Park (HSP) firms listed publicly in Taiwanese stock markets during 2000–2004 and find that the level of knowledge spillovers to sales ranging from 0.166 to 0.525. While this estimation cannot precisely reflect the parameter value of
$B$
in our model, it provides a reasonable reference for the magnitude of spillover effects. Thus, we set the parameter value of
$B$
to 0.2, which is within the range of the findings by Chyi et al. (Reference Chyi, Lai and Liu2012). The model predicts that a larger value of
$B$
will increase the productivity of the education and research sector; more labor will flow to this sector to produce human capital until labor wage equals that in the manufacturing sector. As a result, the long-run equilibrium will be higher because of the higher level of human capital accumulation.
3.2. Parameters in Pollution Function: {
$\eta$
,
$\beta$
}
As described in the manuscript, the natural purification rate
$\eta$
is set to be 0.5. The natural purification rate represents that pollution dissipates or is naturally purified in a certain percentage. Since it depends on various meteorological factors, we do not have sufficient information to calibrate it. For robustness, we further assign different values to
$\eta$
and check how it affects the simulated patterns.
We then calibrate
$\beta$
to fit the facts that firm’s pollution emission intensity is 15.98 kg per 10,000 CNY, defined as
$\frac{\Delta x_{t + 1}}{{A_{d}k_{t}}^{\alpha }\left ({L - l_{ht}} \right )^{1 - \alpha }{h_{t}}^{1 - \alpha }(1-z_{t})}$
, which is constructed based on Environmental Survey and Reporting Database (ESR) from 1998 to 2012. It yields
$\beta =1.98$
. We use chemical oxygen demand (
$COD$
) as a pollution indicator because it is well recorded and commonly targeted by environmental policies. In the revision, as a robustness check, we use sulfur dioxide (
$SO_2$
) as an air pollutant indicator to do the calibration. It yields very similar values for
$\eta$
(0.5) and
$\beta$
(1.91). Furthermore, we conduct a sensitivity analysis so that we can see how the parameterization on parameter
$\eta$
affects the value of parameter
$\beta$
and then how the two parameters affect the simulated pattern. Figure F.2 shows that, given a set of varying
$\beta$
and
$\eta$
, the predictions of the model are generally unchanged.
3.3. Parameters in Disutility: {
${D}$
,
$\gamma$
}
In the environmental literature,
$\frac{\Delta c}{\Delta x}\equiv - \frac{\partial U(c,x)/\partial x}{\partial U(c,x)/\partial c}$
represents the household’s WTP for the environment. Our model follows the conventional theoretical literature to assume a convex disutility function. Ito and Zhang (Reference Ito and Zhang2020) find that a household is willing to pay $1.34 annually to remove 1
$\text{mg}/\text{m}^3$
of air pollution (
$PM_{10}$
). In calibration, parameter
$D$
is standardized to 1 and
$\gamma$
is calibrated to fit the facts that the WTP is $1.34 at steady states. Specifically, the marginal disutility is
$\frac{\partial U(c,x)}{\partial x}=0.68$
and the marginal utility is
$\frac{\partial U(c,x)}{\partial c}=0.24$
at steady states. We assume that the exchange rate between the US dollars and CNY is 7.1, and each household has 3.3 family members as sampled in the China Family Panel Studies Database (CFPS). The simulated moments fit well and yield
$\text{WTP}= \$1.32$
at the steady states.
3.4. Parameters in Production Function: {
$A_{c},A_{d}$
}
We use the firm-level Annual Survey of Industrial Firms (ASIF) database from 1998 to 2007 to construct industrial firms’ total factor productivities (TFPs).
$A_{c}$
and
$A_{d}$
represents the productivity of the manufacturing sector in the clean and dirty economies, respectively. The ASIF database is conducted and maintained by China’s NBS, which covers all state-owned enterprises and all private enterprises with annual sales above 5 million RMB. The total output value included in ASIF accounts for approximately 90% of the total industrial output value of China, covering more than 40 two-digit-code industries. We clean and process the data following the procedure provided by Brandt et al. (Reference Brandt, Van Biesebroeck and Zhang2012): calculating real capital stock by using the perpetual inventory method, deflating the value of inputs, outputs, and wages by four-digit industrial code output deflators and input deflators, and correcting the misrecorded firm information. Even though many approaches can be used to calculate TFP, we choose the commonly used semiparametric algorithms suggested by Levinsohn and Petrin (Reference Levinsohn and Petrin2003), which accounts for the simultaneity and selection biases in estimating the capital and labor coefficients by using intermediates as the proxy for unobservable shocks. According to the official definition by China’s Environmental Protection Agency (MEP), firms in ASIF can be categorized into polluting industries and nonpolluting industries. We set
$A_{c} = 3.25$
and
$A_{d} = 3.32$
in light of the average TFP of polluting industries and nonpolluting industries, respectively.
The remaining set of parameters
$\left \{{\alpha,\delta _{k},\delta _{h},\rho,\sigma,L} \right \}$
is calibrated following the mainstream macroeconomic literature. In China’s economy, labor’s share of value added is 0.55 according to the NBS. Following Hsieh and Klenow (Reference Hsieh and Klenow2009) and Brandt et al. (Reference Brandt, Van Biesebroeck and Zhang2012), we set parameter
$\alpha = 0.5$
. The discount factor is set to
$\rho = 0.96$
to generate a steady-state real interest rate of 0.04. We set the capital depreciation rate and human capital depreciation rate to
$\delta _{h} = 0.05$
and
$\delta _{h} = 0.05$
, respectively. The parameter in the utility function is set to
$\sigma = 0.9$
, implying that the intertemporal substitution elasticity in the CES function is 1.11. Total labor
$L$
in the economy is standardized to 1.
Figure 1. Transition dynamics of four types of economic growth paths.
Notes: The simulation of the four economic paths is based on the calibrated parameters presented in Table 2. In period 0, the dirty economy starts with capital
$k_0=1$
and human capital
$h_0=1$
; the clean economy starts with capital
$k_0=0.1$
and human capital
$h_0=0.1$
.
4. Transition dynamics: short-run and long-run development
In this section, we simulate the transition dynamics of the four types of economic development paths: decentralized dirty economy, social optimal dirty economy, decentralized clean economy, and social optimal clean economy. From the perspective of policy, the whole society concerns about the long-run equilibrium, whereas government officials might place more weight on the short-run dynamics for career promotions. Taking the realistic situation into account, we assume that the dirty economy starts with a higher development level than the clean economy, because the introduction of polluting industries can attract more investors and capitals in the early stage, and it can avoid costly clean production lines and pollution abatement investment, which is a bonus at the expense of environmental quality and natural resources.
In Figure 1, we first focus on the social optimal system and compare the transitional dynamics between the dirty and the clean economies. The model predicts that the dirty path performs better in terms of output and investment in the short run. First, it relies on the assumption that the development of a pollution-intensive industry can attract more capital and human capital in the early stage of development, and the productivity parameter is higher in the polluting industries. The calibrated simulation has taken this assumption into account. While setting the initial value affects the catch-up dynamics, it does not change the model predictions. Second, since pollution decreases the productivity in the education and research sector, and the marginal productivity of labor is higher in the manufacturing sector of the dirty economy, a larger proportion of labor will be endogenously allocated to the manufacturing sector, and it thus contributes a higher level of outputs over the short run. The cost of the short-run prosperity is that human capital accumulation is not sufficient to overrule the diminishing returns to capital, which eventually brings the economy to a zero-growth steady state. Comparatively, in the social optimal clean economy, even though output, consumption, and capital grow slowly in the beginning, they are capable of sustainable growth in the long run because human capital accumulation relaxes the constraint of diminishing returns to capital.
We then focus on the differences between the decentralized and the social optimal dirty economies. In Figure 1, the social optimal dirty economy performs better than the decentralized dirty economy over the long run. This is because the negative externalities of industrial pollution on human capital accumulation is not fully considered in the decentralized scenario. The education and research sector cares about pollution but has no control over it. From a social point of view, firms produce too much pollution in the decentralized dirty economy.Footnote 4 Moreover, an individual education and research institution neglects the fact that an increase in its own human capital stock can contribute to the productivity of the entire sector. From a social point of view, each institution makes inadequate investments into human capital accumulation in the decentralized economy. As a result, the two types of externalities weaken the working productivity in the education and research sector. Comparatively, the social optimal dirty economy is able to the eliminate these externalities by mandating pollution abatement in the manufacturing sector and internalize the spillover effects in the education and research sector. Over the long run, therefore, the decentralized dirty economy falls below the social optimal dirty economy.
5. Policy analysis: switch, taxation, and subsidies
We have so far studied the development paths of dirty and clean economies in different scenarios. This section analyzes how policy interventions change the evolutionary path of a dirty economy. Two types of policy intervention are of interest. First, a successor that takes over a dirty economy and intends to shift the economy to a clean path of development. Second, a policymaker uses tax or subsidy policies to mitigate the adverse effects of pollution on human capital accumulation. This analysis might be of interest to a central government that wants to constrain the local governments’ shortsighted behavior or a local government that attempts to pursue a balance between short-term economic prosperity and environmental protection.
5.1. Switch from a dirty path to a clean path
As shown in Figure 1, the dirty economy is overtaken by the clean economy and finally traps at a low level of development. We assume that a local government can steer its dirty path toward a clean path and save itself from stagnation. Suppose that, on the dirty path, the government decides to switch when the economy starts to stagnate. In addition, we assume that pollution stock from the dirty economy can be gradually and completely removed at an annual purification rate of 0.5.
However, in fact, the transition friction is nontrivial. With regard to market and financial factors, Dong et al., (2022) show that both search friction and financial friction hinder the reallocation of used capital. Also, Dong (Reference Dong2022) proposes that financial friction reduces the matching efficiency in the labor market, especially over business cycles. This implies that capital and labor that have been used in dirty industries can rarely be perfectly employed by clean industries. In addition, the transitioning from dirty resources to clean resources adds another layer of difficulty to the switch. Kambourov and Manovskii (Reference Kambourov and Manovskii2009) find that an employee loses his or her human capital and experiences an 18% drop in wage after the displacement in occupation. For instance, an expert who masters at dirty technology may find difficulties in adapting to a new job in the clean industry. And a dirty production line is almost useless in a clean economy, and it is usually sold at the price of scrap metal. Moreover, the dirty economy also needs to pay a large amount of money for clean technologies and production lines that can support its switch to a clean path, which would further tightens its borrowing constraint and increase the financial friction. Adding up the above costs, we assume that the dirty economy has to sacrifice what it has obtained and switches to the path with a lower economic level compared with the same period of the clean economy.
In Figure 2, the gray lines in the first row show the dynamics and the size of recession during the transition. The economy experiences a dramatic drop and then gradually head toward a transitioned clean path. Another legacy that we should consider is that some types of pollution cannot be completely removed, or the environment is unable to recover from serious damage. We assume that 40% of the pollution stock will remain permanently. As shown in the second row, the existence of permanent pollution makes the growth rate of the transitioned path lower than the case with pollution being completely removed because the long-lasting environmental degradation will permanently reduce the efficiency of human capital accumulation.
Figure 2. The switch to a clean path with pollution removed.
Notes: The simulation of the three economic paths is based on the calibrated parameters presented in Table 2. The first line corresponds to the case where the pollution is completely removed. The second line corresponds to the case where the pollution is partially removed. For the latter scenario, we assume that 40% of the pollution stock will remain permanently.
Figure 2 suggests that switching from a dirty path to a clean path suffers a long period of economic depression. This corresponds to the reason why, in reality, local officials are reluctant to make a structural transition, especially when economic growth links to their career promotion. Even though the central government has incentives to make the transition, the transitioned economy will always lag behind the clean economy. Worse than that, if the environmental damage cannot be completely removed, the transitioned economy will grow even more slowly than the clean economy.
Figure 3. Tax on manufacturing sector.
Notes: The simulation of the two different economic paths is based on the calibrated parameters presented in Table 2. In period 0, the dirty economies start with capital
$k_0=1$
and human capital
$h_0=1$
.
Figure 4. Subsidy on education and research sector.
Notes: The simulation of the two different economic paths is based on the calibrated parameters presented in Table 2. In period 0, the dirty economies start with capital
$k_0=1$
human capital
$h_0=1$
.
Figure 5. Transition dynamics of clean and dirty economic growth paths.
Notes: “Clean” represents a clean economy with zero pollution. “Cal.1” represents a dirty economy with
$\xi =0.781$
which is calibrated to fit the fact that the economic growth rate is 0.069. “Cal.2” represents a dirty economy with
$\xi =0.835$
for comparison.
5.2. Taxation on pollution
The social planner in a dirty economy improves social welfare by fully internalizing two types of externalities: pollution externalities and spillover effects of knowledge. In this section, we discuss how the government addresses the externalities using tax and subsidy policies.
We start with the case of addressing pollution externalities by tax policy. In theory, abatement can be set at a level that exactly internalizes the social costs of pollution, which requires the government to implement a tax rate to induce a social optimal abatement level. However, this is unlikely to happen in the real world because it is politically expensive and almost impossible for a government to predict time-varying external cost of pollution (Hart, Reference Hart2020; Pigou, Reference Pigou1932). For the realistic reasons, we suppose that the government chooses to implement an exogenous tax on pollution generated by manufacturing sector. Figure 3 compares the baseline tax rate
$\phi =1.5$
, depicted by the black solid line, with a higher taxation rate
$\phi =2$
, depicted by the red dashed line. It indicates that the government faces a trade-off between the short-run and the long-run development in the choices of tax rates. While a higher taxation rate reduces pollution and slows down the economy in the short run, it contributes to a higher equilibrium in the long run, because it reduces the harm on the efficiency of human capital accumulation—the engine for long-run growth.
5.3. Subsidy on education and research
To address the spillover effects of knowledge, the subsidy on the education and research sector is helpful to raise the private return of human capital and thereby narrow the gap between private and social benefits. We assume that the government subsidizes
${\psi w}_{ht}$
for each unit of human capital. The total wage of human capital is given by
${\left ( 1 + \psi \right )w}_{ht}h_{t}$
. To avoid other distortions, we assume the subsidy is financed by a lump-sum taxation
${T = \psi w}_{ht}h_{t}$
from the household.
The subsidy essentially changes the relative returns of capital and human capital as well as the household‘s total income. Specifically, the intertemporal decisions on physical capital and human capital yield a non-arbitrage condition between physical capital and human capital,
$r_{t + 1} + 1 - \delta _{k} = \frac{p_{ht + 1}\left ({1 - \delta _{h}} \right ) + w_{ht + 1}}{p_{ht}}$
. The subsidy on
$w_{ht}$
implies that the household will invest more in human capital than physical capital and consumption. In Figure 4, we present the transition dynamics with subsidy rate
$\psi =0.3$
. The subsidy induces a reduction of labor in the manufacturing sector, which is expected to depress the real economy. Nevertheless, a larger proportion of labor allocated to the education and research sector expands human capital stock, which can accelerate economic growth. The two channels work in opposite directions. Figure 4 shows that, with a subsidy on human capital, the short-term economic performance remains almost the same as those in the baseline model. In contrast, the long-run economic performance saliently dominates that in the baseline model. It implies that while the subsidy on human capital can hardly boost the short-run economy, it can lead to an economic boom in the long run.
6. A further discussion
There are alternative ways to model the interaction among the environment, production, and human capital that can make the long-run economic growth sustainable. In reality, this notion is observably true that the economies keep growing even if they adopt a polluting development path. In theory, it is also feasible to model a polluting but sustainable economy as it depends on how outputs generate pollution and to what extent pollution diminishes human capital accumulation.
As a further discussion, we conduct an exercise by modifying certain model assumptions such that, instead of causing economic stagnation, environmental pollution slows down economic growth over the long run. The quantitative results indicate that the economic sustainability in the model depends on whether human capital accumulation will be exhausted by environmental pollution in the long run.
In particular, we allow sustainable long-run growth for the dirty economy by choosing a relatively small value of the parameter
$\xi$
. The simulated transition dynamics are presented in Figure 5. The dirty economy, represented by the gray solid line, starts with higher capital and human capital. Still, it grows noticeably slower than the clean economy, represented by the black solid line. For the comparison, we plot a dotted gray line representing a dirty economy with parameter
$ \xi =0.835$
. It shows that this economy grows slower than the economy with calibrated parameter
$ \xi =0.781$
. If we assign a larger value to
$\xi$
, the dirty economy will stop growing and even decline, implying that sustainability will not occur unless
$\Delta h_{t+1}/h_t$
remains positive in the long run. The above exercise indicates that the model with a dirty economy associated with positive long-run growth has a similar prediction that the polluting development path leads to a short-run boom and a long-run slow or stagnated growth. The description of the model is put in Appendix G.
7. Conclusion
The relationship between economic growth and environmental pollution has been a central concern of environmental economists. Our paper revisits this important topic and propose a dynamic structural model to capture the interaction between economic growth, human capital accumulation, and environmental pollution. We relax two strong assumptions of the EKC: first, there exists no feedback mechanism through which pollution impairs long-run economic growth; second, pollution is reversible as income grows.
We demonstrate that if pollution stock exerts negative effects on human capital accumulation over time, the dirty economy will experience a short-run boom but finally stagnate at a low development level, not following an EKC pattern. We further illustrate that the cost for a dirty economy to switch is expensive and sometimes infeasible if the environmental damage is irreversible. Policy interventions, such as pollution tax or human capital subsidies, help alleviate but will never be able to eradicate this issue.
Local governments may find the EKC argument appealing because temporary economic prosperity is attractive to politicians with tenure constraints. They may also believe that developing regions are too poor to green and therefore follow the “pollute first, remediate later” strategy. However, our theory demonstrates that this strategy lacks wisdom in that it ignores the feedback mechanism of pollution on the long-run economic activities.
APPENDIX A: THE DECENTRALIZED EQUILIBRIUM OF A DIRTY ECONOMY
This section describes the steady states of a decentralized dirty economy based on the model dynamic systems, which are given by equations (1)–(10):
\begin{equation} z^{*} = 1 - \left ({\phi \beta } \right )^{\frac{1}{1 - \beta }}, \end{equation}
\begin{equation} r^{*} = \frac{1}{\rho } - 1 + \delta _{k}, \end{equation}
\begin{equation} l_{h}^{*} = \frac{\delta _{h}L}{\frac{1}{\rho } - 1 +{2\delta }_{h}}, \end{equation}
\begin{equation} l_{y}^{*} = L - l_{h}^{*}, \end{equation}
\begin{equation} x^{*} = \left ( \frac{Bl_{h}^{*}}{\delta _{h}} \right )^{\frac{1}{\xi }} - 1, \end{equation}
\begin{equation} k^{*} = \frac{\eta x^{*}\alpha \left ( \left ({1 - z^{*}} \right )^{1 - \beta } - \phi \right )}{r^{*}}, \end{equation}
\begin{equation} h^{*} = \left [\frac{r^{*}}{\left ( \left ({1 - z^{*}} \right ) - \phi \left ({1 - z^{*}} \right )^{\beta } \right )\alpha A_d} \right ]^{\frac{1}{1 - \alpha }}\frac{k^{*}}{l_{y}^{*}}, \end{equation}
\begin{equation} y^{*} = Ak_{t}^{*\alpha }h_{t}^{*1 - \alpha }l_{yt}^{*1 - \alpha }\left ( 1 - z^{*} \right ), \end{equation}
\begin{equation} c^{*} = y^{*} - \delta _{k}k^{*}. \end{equation}
APPENDIX B: THE SOCIAL OPTIMAL EQUILIBRIUM OF A DIRTY ECONOMY
This section describes a social optimal dirty economy. A social planner maximizes the social benefit:
\begin{equation*} \underset {\{{c_{t},{l}_{ht},k_{t + 1},h_{t + 1},x_{t + 1}}\}}{\max }{\sum \limits _{t = 0}^{\infty }{\rho ^{t}\left ( \frac {c_{t}^{1 - \sigma } - 1}{1 - \sigma } -\frac {D{x_{t}}^{\gamma }}{\gamma } \right )}} \end{equation*}
which subjects to the budget constraint:
\begin{equation} c_{t} + k_{t + 1} - \left ({1 - \delta _{k}} \right )k_{t} = A_{d}k_{t}^{\alpha }h_{t}^{1 - \alpha }{l_{yt}}^{1 - \alpha }\left ({1 - z_{t}} \right ), \end{equation}
the law of motion of human capital accumulation:
\begin{equation} h_{t + 1} = Bl_{ht}{\left ({1 + x_{t}} \right )^{- \xi }h}_{t} +{\left ({1 - \delta _{h}} \right )h}_{t}, \end{equation}
and the law of motion of pollution accumulation:
\begin{equation} x_{t + 1} ={A_{d}k_{t}}^{\alpha }\left ({L - l_{ht}} \right )^{1 - \alpha }{h_{t}}^{1 - \alpha }\left ({1 - z_{t}} \right )^{\beta } + \left ({1 - \eta } \right )x_{t}. \end{equation}
Denoting
$\lambda _{t}$
,
$p_{t}$
, and
$q_{t}$
as the Lagrangian multipliers of the last three constraints correspondingly, the optimal conditions for
$c_{t}$
,
$z_{t}$
,
$l_{ht}$
,
$k_{t+1}$
,
$h_{t+1}$
, and
$x_{t+1}$
are given by:
\begin{equation} c_{t}^{-\sigma } =\lambda _{t}, \end{equation}
\begin{equation} \lambda _{t} =q_{t}\beta (1-z_{t})^{\beta -1}, \end{equation}
\begin{align} {p_{t}B{\left ({1+x_{t}}\right ) ^{-\xi }h}_{t}}&{=\lambda _{t}A_{d}{\left ({1-\alpha }\right ) k}_{t}^{\alpha }\left ({L-l_{ht}}\right ) ^{-\alpha }{h_{t}}^{1-\alpha }\left ({1-z_{t}}\right ) } \nonumber \\[5pt] &\quad{-q_{t}{A_{d}\left ({1-\alpha }\right ) k}_{t}^{\alpha }\left ({L-l_{ht}}\right ) ^{-\alpha }{h_{t}}^{1-\alpha }\left ({1-z_{t}}\right ) ^{\beta },} \end{align}
\begin{align} {\frac{1}{\rho }\lambda _{t}}&{=\lambda _{t+1}\left [{A_{d}\alpha k_{t+1}^{\alpha -1}\left [{L-l_{ht+1}}\right ] ^{1-\alpha }{h_{t+1}}^{1-\alpha }\left [{1-z_{t+1}}\right ] +1-\delta _{k}}\right ] } \nonumber \\[5pt] &\quad{-q_{t+1}A_{d}\alpha k_{t+1}^{\alpha -1}\left ({L-l_{ht+1}}\right ) ^{1-\alpha }{h_{t+1}}^{1-\alpha }\left ({1-z_{t}}\right ) ^{\beta },} \end{align}
\begin{align} {\frac{1}{\rho }p_{t}}&{=\lambda _{t+1}A_{d}{\left ({1-\alpha }\right ) k}_{t+1}^{\alpha }\left ({L-l_{ht+1}}\right ) ^{1-\alpha }{h_{t+1}}^{-\alpha }\left ({1-z_{t+1}}\right ) } \nonumber \\[5pt] &\quad{-q_{t+1}A_{d}{\left ({1-\alpha }\right ) k}_{t+1}^{\alpha }\left ({L- l_{ht+1}}\right ) ^{1-\alpha }{h_{t+1}}^{-\alpha }\left ({1-z_{t+1}}\right ) ^{\beta }} \nonumber \\[5pt] &\quad{+p_{t+1}\left [{Bl_{ht+1}\left [{1+x_{t}}\right ] ^{-\xi }+1-\delta _{h}}\right ],} \end{align}
\begin{equation} \frac{1}{\rho }q_{t} = Dx_{t+1}^{\gamma -1}+p_{t+1}B\xi \left ({1+x_{t}}\right ) ^{-\xi -1}l_{ht+1}h_{t+1}+q_{t+1}\left ({1-\eta }\right ). \end{equation}
Equations (B1)–(B9) define the dynamic system of a social optimal dirty economy. The steady states are given by:
\begin{align*} &x^{\ast } =\left ( \frac{BL}{\frac{1}{\rho }-1+\delta _{h}}\right ) ^{\frac{1}{\xi }}-1, \\[5pt] &l_{h}^{\ast } =\frac{\delta _{h}L}{\frac{1}{\rho }-1+\delta _{h}}, \\[5pt] &k^{\ast } =\frac{\frac{\beta -1}{\beta }\alpha \eta x^{\ast }\left ( 1-z^{\ast }\right ) ^{1-\beta }}{\frac{1}{\rho }-1+\delta _{k}}, \\[5pt] &z^{\ast } =1-\left [ \eta x^{\ast }\left ( 1-\frac{\frac{\beta -1}{\beta }\alpha \delta _{k}}{\frac{1}{\rho }-1+\delta _{k}}\right ) \right ] ^{\frac{\sigma }{{({1-\beta })}{({1-\sigma })}}}\left ( q^{\ast }\beta \right ) ^{\frac{1}{(1-\beta )(1-\sigma )}}, \\[5pt] &y^{\ast } ={A_{d}k}^{\alpha \ast }h^{\ast 1-\alpha }{l_{y}}^{\ast 1-\alpha }\left ({1-z^{\ast }}\right ), \\[5pt] &h^{\ast } =\left ({\eta x^{\ast }}\right ) ^{\frac{1}{1-\alpha }}k^{\ast -\frac{\alpha }{1-\alpha }}\left ( L-l_{h}^{\ast }\right ) ^{-1}\left ( 1-z^{\ast }\right ) ^{\frac{-\beta }{1-\alpha }}{A_{d}}^{-\frac{1}{1-\alpha }}, \\[5pt] &c^{\ast } =y^{\ast }-\delta _{k}k^{\ast }. \end{align*}
APPENDIX C: THE DECENTRALIZED EQUILIBRIUM OF A CLEAN ECONOMY
This section describes a decentralized dirty economy.
C.1. HOUSEHOLD
The household’s maximization problem is given by:
\begin{equation*} \underset {\left \{ c_{t},k_{t+1},h_{t+1}\right \} }{\max }{\sum \limits _{t=0}^{\infty }\rho ^{t}}\frac {c_{t}^{1-\sigma }-1}{1-\sigma }, \end{equation*}
subject to the budget constraint:
\begin{equation} {c_{t}+k_{t+1}-\left ({1-\delta _{k}}\right ) k_{t}+p_{ht}\left [{h_{t+1}-\left [{1-\delta _{h}}\right ] h_{t}}\right ] ={r_{t}k}_{t}+w_{yt}(l_{yt}+l_{ht})+w_{ht}h_{t}+\pi _{yt}+\pi _{ht}.} \end{equation}
The optimal conditions for
$c_{t}$
,
$k_{t+1}$
, and
$h_{t+1}$
are given by:
\begin{equation} c_{t}^{-\sigma } =\lambda _{t}, \end{equation}
\begin{equation} \lambda _{t} =\rho \lambda _{t+1}\left ({r_{t+1}+1-\delta _{k}}\right ), \end{equation}
\begin{equation} p_{ht}\lambda _{t} =\rho \lambda _{t+1}\left [{p_{ht+1}\left [{1-\delta _{h}}\right ] +w_{ht+1}}\right ]. \end{equation}
The household’s optimal problem no longer suffers pollution disutility in the clean scenario.
C.2. FIRMS
A representative firm’s maximization problem is given by:
\begin{equation*} \underset {\{{k_{t},l_{yt},h_{t}}\}}{\max }{\pi _{yt}=A_{c}k}_{t}^{\alpha }h_{t}^{1-\alpha }{l_{yt}}^{1-\alpha }-r_{t}k_{t}-w_{yt}l_{yt}-w_{ht}h_{t}. \end{equation*}
The optimal conditions for
$k_{t}$
,
$l_{yt}$
, and
$h_{t}$
are given by:
\begin{equation} r_{t} ={A_{c}\alpha k}_{t}^{\alpha -1}h_{t}^{1-\alpha }{l_{yt}}^{1-\alpha }, \end{equation}
\begin{equation} w_{yt} ={A_{c}\left ({1-\alpha }\right ) k}_{t}^{\alpha }h_{t}^{1-\alpha }{l_{yt}}^{-\alpha }, \end{equation}
\begin{equation} w_{ht} ={A_{c}\left ({1-\alpha }\right ) k}_{t}^{\alpha }h_{t}^{-\alpha }{l_{yt}}^{1-\alpha }. \end{equation}
C.3. EDUCATION AND RESEARCH
An individual institution’s maximization problem is given by:
\begin{equation*} \pi _{i,ht}=\max _{\{l_{i,ht}\}}p_{ht}Bl_{i,ht}h_{t}-w_{yt}l_{i,ht}. \end{equation*}
The optimal condition with respect to
$l_{ht}$
is given by:
\begin{equation} p_{ht}Bh_{t}=w_{yt}. \end{equation}
Equations (C1)–(C8) define the full dynamic of the decentralized clean economy, which yields the BGP:
$\frac{y_{t + 1}}{y_{t}} = \frac{c_{t + 1}}{c_{t}} = \frac{k_{t + 1}}{k_{t}} = \frac{h_{t + 1}}{h_{t}} = BL - r^{*} - 2\delta _{h} + \delta _{k} + 1$
. In equilibrium, labor allocations between the manufacturing and education and research sectors are given by
$l_{yt}^{*} =\frac{r^{*} + \delta _{h} - \delta _{k}}{B}$
and
$l_{ht}^{*} = L - l_{yt}^{*}$
.
APPENDIX D: THE SOCIAL OPTIMAL EQUILIBRIUM OF A CLEAN ECONOMY
This section describes a social optimal clean economy. The social planner’s maximization problem is given by:
\begin{equation*} \underset {\left \{ c_{t},k_{t+1},h_{t+1}\right \} }{\max }{\sum \limits _{t=0}^{\infty }\rho ^{t}}\frac {c_{t}^{1-\sigma }-1}{1-\sigma }, \end{equation*}
which subjects to the budget constraint:
\begin{equation} c_{t}+k_{t+1}-\left ({1-\delta _{k}}\right ) k_{t}={A_{c}k}_{t}^{\alpha }h_{t}^{1-\alpha }{l_{yt}}^{1-\alpha }, \end{equation}
and the law of motion of human capital accumulation:
\begin{equation} h_{t+1}=Bl_{ht}h_{t}+{\left ({1-\delta _{h}}\right ) h}_{t}. \end{equation}
The optimal conditions with respect to
$c_{t}$
,
$l_{ht}$
,
$k_{t+1}$
, and
$h_{t+1}$
are given by:
\begin{equation} c_{t}^{-\sigma } =\lambda _{t}, \end{equation}
\begin{equation} p_{t}Bh_{t} =\left ({1-\alpha }\right ) \lambda _{t}A_{c}k_{t}^{\alpha }h_{t}^{1-\alpha }\left ({L-l_{ht}}\right ) ^{-\alpha }, \end{equation}
\begin{equation} \lambda _{t} =\rho \lambda _{t+1}\alpha Ak_{t+1}^{\alpha -1}h_{t+1}^{1-\alpha }\left ({L-l_{ht+1}}\right ) ^{1-\alpha }+1-\delta _{k}, \end{equation}
\begin{equation} p_{t} =\rho \lambda _{t+1}\left ({1-\alpha }\right ) A_{c}k_{t+1}^{\alpha }h_{t+1}^{-\alpha }\left ({L-l_{ht+1}}\right ) ^{1-\alpha }+\rho p_{t+1}\left ({Bl_{ht+1}+1-\delta _{h}}\right ). \end{equation}
Equations (D1)–(D6) define the full dynamic of the decentralized clean economy, which yields the BGP:
$\frac{y_{t+1}}{y_{t}}=\frac{c_{t+1}}{c_{t}}=\frac{k_{t+1}}{k_{t}}=\frac{h_{t+1}}{h_{t}}=\left [ \rho \left ({BL+1-\delta _{h}}\right ) \right ] ^{\frac{1}{\sigma }}$
.
APPENDIX E: TRANSITION DYNAMICS OF A CLEAN ECONOMY
In the equilibrium of a clean economy, the labor allocations
$\left \{{l_{ht}, l_{yt}} \right \}$
, c-k ratio
$\frac{c_{t}}{k_{t}}$
, and k-h ratio
$\frac{k_{t}}{h_{t}}$
remain stable on the BGP. We rearrange the model and construct a new dynamic system through which, as long as the labor allocation, c-k ratio, and k-h ratio converge to their own steady states, the clean economy will reach its BGP.
The reconstructed dynamic of the decentralized clean economy from equations (C1)–(C8) is given by:
\begin{equation} \frac{c_{t}}{k_{t}}+\frac{k_{t+1}}{k_{t}}-\left ({1-\delta _{k}}\right ) =A_{c}\left ( \frac{k_{t}}{h_{t}}\right ) ^{\alpha -1}l_{yt}^{1-\alpha }, \end{equation}
\begin{equation} \frac{h_{t+1}}{h_{t}} =B{\left ({1+x_{t}}\right ) ^{-\xi }l}_{ht}+1-\delta _{h}, \end{equation}
\begin{equation} \left ( \frac{c_{t+1}}{c_{t}}\right ) ^{\sigma } =\left ( \frac{\lambda _{t+1}}{\lambda _{t}}\right ) ^{-1}, \end{equation}
\begin{equation} \left ( \frac{\lambda _{t+1}}{\lambda _{t}}\right ) ^{-1} =\rho \left ({r_{t+1}+1-\delta _{k}}\right ), \end{equation}
\begin{equation} \frac{\frac{c_{t}}{k_{t}}}{\frac{c_{t+1}}{k_{t+1}}} =\left ( \frac{c_{t+1}}{c_{t}}\right ) ^{-1}\frac{k_{t+1}}{k_{t}}, \end{equation}
\begin{equation} r_{t} =\alpha A_{c}\left ( \frac{k_{t}}{h_{t}}\right ) ^{\alpha -1}l_{yt}^{1-\alpha }, \end{equation}
\begin{equation} p_{ht}B\left ({1+x_{t}}\right ) ^{-\xi } =\left ({1-\alpha }\right ) A_{c}\left ( \frac{k_{t}}{h_{t}}\right ) ^{\alpha }l_{yt}^{-\alpha }. \end{equation}
Equations (E1)–(E7) define a new dynamic system through which the decentralized clean economy finds its transition dynamic and BGP given an arbitrary starting point.
In the social optimal clean economy, similarly, we rearrange the dynamic represented by equations (D1)–(D6) as:
\begin{align} \frac{k_{t+1}}{k_{t}} =A_{c}\left ( \frac{k_{t}}{h_{t}}\right ) ^{\alpha -1}\left ({L-l_{ht}}\right ) ^{1-\alpha }+1-\delta _{k}-\frac{c_{t}}{k_{t}}, \end{align}
\begin{align} \frac{k_{t+1}}{k_{t}} =B{\left ({1+x_{t}}\right ) ^{-\xi }l}_{ht}+1-\delta _{h}, \end{align}
\begin{align} \left ( \frac{c_{t+1}}{c_{t}}\right ) ^{\sigma } =\rho \left [{\alpha A_{c}\left ( \frac{k_{t+1}}{h_{t+1}}\right ) ^{\alpha -1}\left ({L-l_{ht+1}}\right ) ^{1-\alpha }+1-\delta _{k}}\right ], \end{align}
\begin{align} \rho \left [{B\left ({1+x_{t}}\right ) ^{-\xi }L+1-\delta _{h}}\right ] =\left ( \frac{c_{t+1}}{c_{t}}\right ) ^{\sigma }\left ( \frac{k_{t}}{h_{t}}\right ) ^{\alpha }\left ( \frac{k_{t+1}}{h_{t+1}}\right ) ^{-\alpha }\left ( \frac{L-l_{ht+1}}{L-l_{ht}}\right ) ^{\alpha }, \end{align}
\begin{align} \frac{c_{t}/k_{t}}{c_{t+1}/k_{t+1}} =\left ( \frac{c_{t+1}}{c_{t}}\right ) ^{-1}\frac{k_{t+1}}{k_{t}}, \end{align}
\begin{align} x_{t+1} =\left ({1-\eta }\right ) x_{t}. \end{align}
Equations (E8)–(E13) define a new dynamic system through which the social optimal clean economy finds its transition dynamic and BGP given an arbitrary starting point.
APPENDIX F: SENSITIVITY ANALYSIS ON PARAMETERS
This section presents sensitive analysis on parameters
$\left \{{\xi, \beta } \right \}$
, which are closely related to the key mechanism that how pollution generates and affects the economic dynamics.
Parameter
$\xi$
corresponds to the negative effects of pollution on human capital accumulation. In Section 3, it is empirically calibrated by how air pollution (
$PM_{2.5}$
) affects the productivity of human capital, using the two-stage least square method with thermal inversion as an instrumental variable. Figure F1 presents the sensitivity analysis of parameter
$\xi$
. A larger value of
$\xi$
diminishes human capital accumulation to a larger extent. In the short run, the economic path is a bit higher than the baseline because the equilibrium condition of labor wage leads to a large proportion of labor flowing to final goods production. However, in the long run, less human capital accumulation leads to a significantly lower economic equilibrium than the baseline. Within a certain range of
$\xi$
, the economic dynamics change systematically and the predictions of the model still hold.
Figure F1. Sensitivity analysis on parameter
$\xi$
.
Notes: The simulation is based on decentralized economy scenario. The black and the red solid lines describe the baseline decentralized clean and dirty economies, respectively, as presented in Figure 1.
Furthermore, we conduct a sensitivity analysis on how the parameterization on parameter
$\eta$
affects the value of parameter
$\beta$
and then how the two parameters affect the simulated pattern. We assign different values to parameter
$\eta$
and compute the corresponding values of parameter
$\beta$
. Figure F2 shows that a lower
$\eta$
leads to a higher
$\beta$
, implying that pollution accumulates faster and the productivity of education and research sector is reduced much more, and thus more labor will flow to the manufacturing sector. While it promotes the short-run economy, the long-run economic equilibrium is relatively lower because it leads to a lower level of human capital accumulation. As a result, given a set of varying
$\beta$
and
$\eta$
, the predictions of the model are generally unchanged.
Figure F2. Sensitivity analysis on parameter
$\beta$
.
Notes: The simulation is based on decentralized economy scenario. The black and the red solid lines describe the baseline decentralized clean and dirty economies, respectively, as presented in Figure 1.
APPENDIX G: A POLLUTING AND SUSTAINABLE ECONOMY
In this model, a social planner maximizes social benefit:
\begin{equation} \max _{\{c_t, s_t, k_{t+1},h_{t+1}\}}\sum _{t=0}^\infty \rho ^t\Big (\frac{c_t^{1-\sigma }-1}{1-\sigma }\Big), \end{equation}
which subjects to the budget constraint:
\begin{equation} c_{t} + k_{t + 1} - \left ({1 - \delta _{k}} \right )k_{t} = Ak_{t}^{\alpha }h_{t}^{1 - \alpha }{L_t}^{1 - \alpha }\left ({1 - s_{t}} \right ), \end{equation}
and the law of motion of human capital accumulation:
\begin{equation} h_{t + 1} = By_{t}s_{t}-\xi x_{t} + (1 - \delta _{h})h_{t}. \end{equation}
The notations remain the same as the manuscript. The production function is given by
$y_t=Ak_{t}^{\alpha }h_{t}^{1 - \alpha }{L_t}^{1 -\alpha }$
. Production is used for consumption, physical capital accumulation, and human capital accumulation.
$s_t$
denotes the share of production allocated to human capital accumulation. We assume that pollution function
$x_t=y_t$
. In the process of human capital accumulation, a proportion of the allocated production
$y_t s_t$
pays for pollution-caused medical care, preventive protection, and work inefficiency (such as work absenteeism, loss of concentration, and less skilled employees a result of environmental pollution), which is assumed to be proportional to environmental pollution.
The general equilibrium comprises the BGP of consumption
$c_t$
, capital
$k_t$
, human capital
$h_t$
, pollution
$x_t$
, and output
$y_t$
, and production allocation share
$s_t$
. The main parameters are consistent with the manuscript, except that
$\xi =0.781$
due to the different setup. To calibrate parameter
$\xi$
, we use environmental pollution (
$PM_{2.5}$
) between 2000 and 2012 to compute the average county-year level growth rate of pollution (0.032), which implies that
$\xi =0.835$
. The
$PM_{2.5}$
value is obtained from National Aeronautics and Space Administration (NASA) and aggregated from grid level to county-year level. We choose the period prior to 2012 because the China’s Action Plan of Air Pollution Prevention and Control was implemented in 2013. As a robustness check, the model implies that
$\xi =0.781$
if we assume that the growth rate of pollution equals to 0.06 which is closer to China’s average real GDP growth rate between 2000 and 2012.
