Sustainability Traps: Patience and Innovation

Abstract

This paper argues that the joint relation between long-term orientation, environmental quality and innovation plays a key role in explaining the economic and the environmental dimension of sustainability. In our model multiple equilibria of economic development and environmental quality can arise due to a trade-off between the demand for innovation that promotes sustainability, and the ephemeral pleasure from polluting manufacturing that impedes it. Additional to traditional policies such as aid and technology transfers, policies that target behavioral changes through environmental protection may provide a double-dividend of economic and environmental sustainability through an environment-patience-innovation channel.

1 Introduction

There is extensive literature documenting that while some countries thrive both, economically and environmentally, others stagnate in an “environmental and economic poverty trap” (Fact 1).¹ At the same time evidence shows that even if technological advancements and income increases exist in countries that face such a trap—through aid, imitation or technology transfer—these are not capable to help those countries out of it (Fact 2).² Yet the views in the literature on the factors behind both Facts 1 and 2 are broad. This paper aims at narrowing this gap through an R&D-driven endogenous growth model where long-term orientation positively depends on the quality of the local natural environment. This, in turn, affects the decisions of individuals for investments in research-intensive, yet sustainability-promoting technologies (that take time to develop), against the instant but ephemeral gratification from less R&D-intensive and polluting consumption, which reinforces a vicious cycle of low growth and low environmental quality.

Figures 1 and 2 below document the previous facts that motivate our analysis, and introduce our main mechanism. A key variable in our framework is the quality of the local natural environment which we proxy by the Environmental Performance Index (EPI).³ For a cross section of 133 countries, Fig. 1 plots R&D expenditure (as a percentage of GDP) against GDP per capita. Panel (a) shows countries that feature EPI, N, below a certain threshold $N^*$, while panel (b) shows countries with $N>N^*$. For countries with $N>N^*$ higher income is associated with higher expenditure in R&D in a statistically significant manner, which does not hold true for countries with $N<N^*$, where the correlation is low and statistically insignificant.⁴ In the same figure, the size of the circles around countries shows a measure of the (relative) rate of time preference (RTP) for 76 of the countries in the sample, as provided by Falk et al. (2018).⁵

Figure 2 plots the R&D expenditure against the EPI grouping countries by the same threshold of environmental performance; again circles measure long-term orientation.

Fig. 1

R&D expend. (%GDP) vs GDP p.c. ($N^*=56$) The line shows the linear regression fit. Sources: R&D expend., GDP p.c. World Bank Indicators; EPI Score, EPI (2018); RTP, Falk et al. (2018)

Fig. 2

R&D expend. (%GDP) vs EPI ($N^*=56$) The line shows the linear regression fit. Sources: R&D expend., GDP p.c. World Bank Indicators; EPI Score, EPI (2018); RTP, Falk et al. (2018)

The main messages that Figs. 1 and 2 convey are the following: Fig. 1 shows that countries with environmental performance beyond the threshold $N^*$ are more long-term oriented (larger circles), with a positive tendency to translate higher income to more innovation efforts; for the same group of countries, Fig. 2 shows that the higher is the quality of the local natural environment, the higher is the activity in R&D. On the contrary, the group of countries with environmental performance below the threshold $N^*$ (left panel of Figs. 1 and 2) may face a sustainability trap with low environmental quality, low GDP per capita, low level of R&D and low level of patience.

In our model, first, we investigate the importance of this environment-patience-innovation channel for sustainability and we capture the aforementioned threshold of environmental quality $N^*$. Second, consistent with the data of Fig. 1 our model shows that exogenous income increases in countries with $N<N^*$ (left panel), may not help them escape the sustainability trap unless development policies undertaken are coupled with environmental protection. Notably, the previous figures are used to motivate our analysis and not to infer causality. Endogeneity between environmental quality, time preference, R&D and GDP per capita is possible. To this end, our dynamic general equilibrium framework considers the endogenous relations among those variables and, in turn, expands the set of mechanisms that can lead to multiple equilibria of sustainability.

The literature has so far proposed various factors behind poverty traps. Barrett et al. (2016) offer an extensive review on these factors; weak institutions, coordination and market failures, structural barriers to adopt more advance technologies, limited access to capital markets and backward social norms are some that act on limiting capital accumulation. In addition, and relevant to our model, the authors also put forth psychological factors like higher risk aversion and shorter planning horizons of poorer individuals as limiting for growth, and highlight the importance of natural capital for the process of development. However, as they state, the literature on poverty traps through feedbacks with natural resources is “strikingly thin", which is where we contribute. In Schaefer (2019) poor environmental conditions increase children’s mortality and impose a drag on growth because they deter households from investing in the human capital of the future generation. The likelihood of poverty traps is governed by environmental degradation through its effect on longevity also in Varvarigos (2010). The extend to which a developing country rich in natural resources can escape a poverty trap is studied in Le Van et al. (2010) and Antoci et al. (2010). In the former paper the resource is a depletable one and the poverty trap arises due to a convex-concave production function, while in the latter the resource is renewable and the trap arises due to its logistic function and decreasing returns to scale in the production of the final good. In this paper we keep all standard assumptions for the concavity of the production technology, instantaneous utility, and for the dynamics of the natural environment (our depletable natural resource).

The aforementioned positive relationship between environmental quality and long-term orientation, which is an important element of our theory, finds also support in the literature. Lower environmental quality is linked to lower life expectancy,⁶ while people that face higher probability of death are more oriented towards the present and discount the future more (Blanchard 1985). Also, from a long-run perspective, Galor and Özak (2016) attribute the deep rooted part of time preference to environmental conditions. They document that populations exposed to good climatic conditions in the pre-industrial era developed a positive attitude towards the long-term, and, therefore, towards investments in agricultural technologies of the time. In our framework history is important as the initial condition of the natural environment matters for the uniqueness of equilibria and the differential response of economic variables to productivity and income shocks.⁷ Figure 3 zooms in the positive relationship between the contemporary rate of time preference and the quality of the natural environment, the EPI score, of Fig. 2.

Fig. 3

RTP vs EPI. The solid line shows the linear regression fit. Sources: EPI Score, EPI (2018); RTP, Falk et al. (2018)

To the best of our knowledge, this is the first paper that discusses the joint interaction of investment in innovation, patience (endogenous) and the quality of the natural environmental. To capture the observed joint correlations of Figs. 1 and 2 between the quality of the local environment, innovation, long-term orientation, and economic development, we develop an R&D-based model of endogenous growth with technological quality improvements, where environmental degradation affects the investment decisions of individuals in innovation through endogenous time preferences. In our model, manufacturing activities can be of different grades of technological and environmental quality, with higher grades requiring higher R&D activity of more patient agents. This leads to higher productivity and lower emissions intensity of manufacturing, thus promoting both, the economic and environmental dimension of sustainability.⁸ When the long-term orientation of agents depends on the environment, two equilibria arise: one with high levels of environmental quality and economic growth, and one with low environmental quality and growth. Additionally, albeit stylized, our model captures the fact that exogenous income increases (through e.g. technology transfers that increase the productivity of the economy’s growth engine) unambiguously improve the situation of economies in the high equilibrium with respect to both, the natural and the economic environment, while may worsen the situation of countries in the low equilibrium and reproduces the non-monotonic relation that appears in Figs. 1 and 2. This result has important policy implications that we discuss in our conclusion.

The remainder of the paper is organized as follows. Section 2 presents the model. It develops the endogenous growth framework and shows the equilibrium conditions of our stylized economy. Section 3 deals with comparative statics and simulations. In this section we show the existence of multiple equilibria, perform stability analysis, and compare the development of economies based on initial conditions and long-term views, when these economies face exogenous productivity increases. Section 4 concludes.

2 The Model

To establish the link between the natural environment and economic development in the modern era, we use an R&D-based endogenous growth framework with research to improve the quality of firm-specific technological processes. Our model, albeit highly stylized, captures the trade-off between the demand for immediate production of low technological (and environmental) quality, versus technology-advanced production—which is cleaner and has higher productivity, but is based on innovation that takes time. When allowing for the intertemporal discount rate of the representative household to depend on the quality of the environment it lives in, the model generates two equilibria of development: one with high environmental quality and growth, and one with low environmental quality and growth prospects. Below we present our model in detail.

2.1 Firms

As in Acemoglu and Cao (2015) and Akcigit and Kerr (2018)–among others–there is a continuum of intermediate firms, indexed by $j \in [0,1]$, each associated with a certain technological quality level $q_j$. The final good sector combines the output of these firms $x_j$ with labor $L_Y$ to produce the final good Y in a Cobb-Douglas fashion. Final good production follows:

$$\begin{aligned} Y_t= L_{Yt}^{1-\beta }\int _0^1q_{jt}^{1-\beta } x_{jt}^{\beta }dj, \qquad j \in [0,1], \end{aligned}$$

(1)

with $\beta \in [0,1]$. Ceteris paribus, higher technological quality of intermediate inputs translates into a higher productivity in manufacturing. The final good is produced in competition with input prices taken as given. We normalize the price of Y to be one in every period. Hence profit maximization yields the following demand curves for labor $L_Y$ and intermediates $x_j$, respectively:

$$\begin{aligned} w_t=(1-\beta ) Y_t/L_{Yt}, \end{aligned}$$

(2)

$$\begin{aligned} p_{jt}= \beta L_{Yt}^{1-\beta } q_{jt}^{1-\beta } x_{jt}^{\beta -1}, \end{aligned}$$

(3)

where w denotes the wage rate of labor and $p_{j}$ the consumer price of intermediate j.

The CES composite in (1) supports monopolistic competition in the production of intermediates. We assume that each good j is produced by one monopolistic firm and each firm produces one good; the marginal cost of producing intermediate $x_j$ is $\psi$ units of the final good, with $\psi >0$ a constant. Additional to the production of intermediates, each firm j is responsible for improving upon its existing technological level by performing R&D in-house.⁹ To do so it combines firm-specific technology $q_j$ with $l_{j}$ units of skilled labor with the following specification,

$$\begin{aligned} \dot{q}_{jt}= A q_{jt} l_{jt}, \end{aligned}$$

(4)

with $A>0$ a productivity parameter and $q_{j0}=q_{0}>0$, given.¹⁰ We assume that an exogenous positive change in A can occur through international technology transfers, foreign aid or imitation, all promoting the productivity of R&D activity—the growth engine in this framework.

The objective of each intermediate monopolist is the maximization of its discounted stream of monopoly profits ($\pi _j=p_j x_j- \psi x_j$) net of expenditure in improving its technology ($w l_j$) while taking into account the demand curve (3), i.e.,

$$\begin{aligned} \max _{\{x_{jt}, l_{jt}\}_{t=0}^{\infty }}\int _0^\infty \left[ \beta L_{Yt}^{1-\beta } q_{jt}^{1-\beta } x_{jt}^{\beta }- \psi x_{jt}-w_t l_{jt}\right] e^{-\int _0^t r_s ds} dt, \end{aligned}$$

and subject to (4); r is the interest rate at which future cash flows are discounted. Without loss of generality we normalize $\psi =\beta ^2$ as in Acemoglu (2002). With $V_j=\lambda _j q_j$ the stock market valuation of firm j ($\lambda _j$ is the shadow price for the firm specific technology $q_j$), this optimization implies:

$$\begin{aligned} x_{jt}=q_{jt}L_{Yt}, \end{aligned}$$

(5)

$$\begin{aligned} V_{jt}= V_t=w_t/A, \end{aligned}$$

(6)

$$\begin{aligned} \frac{\pi _{jt}}{V_t}+\frac{\dot{V}_t}{V_t}=r_t. \end{aligned}$$

(7)

The same valuation across firms implies that $\pi _j=\pi , x_j=x, q_j=q, l_j=L_S$ (with $L_S$ total scientific labor), $\pi =\beta (1-\beta )q L_Y$ and $x=q L_Y$ for all j.

According to Eq. (7) asset markets are in equilibrium.¹¹ Moreover, in equilibrium total output Y is allocated to aggregate consumption C and aggregate expenditure in intermediates I, i.e., $Y=C+I$. With the above, aggregate expenditure in intermediates reads $I=\int _0^1\psi x_{j}dj=\beta ^2 Q L_Y$, with $Q \equiv \int _0^1q_j dj$, the average technological level of the economy, and thus $q=Q$. From (1) and (5), final good production is $Y=Q L_Y$ and from the resource constraint of this economy, aggregate consumption $C=(1-\beta ^2) Y$. Equation (2) also implies $w=(1-\beta ) Q$. Combining (6) and (7) gives:

$$\begin{aligned} r_t= \beta A L_{Yt} + \frac{\dot{Q}_t}{Q_t}. \end{aligned}$$

(8)

2.2 Emissions and the Environment

For our purposes, final good production creates polluting by-products–henceforth emissions–E, which deteriorate the quality of the local environment N. Its law of motion reads:

$$\begin{aligned} \dot{N_t}=-E_t +(1-\delta )(\bar{N}-N_t), \end{aligned}$$

(9)

with a given initial level of environmental quality $N_0>0$, $\bar{N}>0$ the highest attainable level of environmental quality (e.g. pre-industrial levels), and $\delta \in (0,1)$ the degree of environmental persistence.¹²

Let us denote with $E=\phi (\cdot ) Y$ the level of emissions in each period and with $\phi (\cdot )>0$ the emissions intensity of production. Similar to Nordhaus and Boyer (2000), and Bosetti et al. (2006), we assume the gradual and costless improvement of the emissions intensity of production; particularly, closer to Bosetti et al. (2006), it benefits from higher levels of economy-wide technology in an Arrow (1962) “learning-by-doing" fashion, i.e. $\phi (Q)$ with $\phi '(Q)<0$ and $\phi ''(Q)>0$. For a balanced growth path to exist, we employ $\phi (Q) =\varphi Q^{-1}$, $\varphi >0$, such that effective emissions read $E=\varphi Y/Q$, and with $Y=Q L_Y$, $E=\varphi L_Y$.¹³ Emissions, then, deplete the stock of natural environment N according to:

$$\dot{N}_{t} = - \varphi L_{{Yt}} + (1 - \delta )(\bar{N} - N_{t} ).$$

(9′)

Let $L_Y^{SS}$ and $L_S^{SS}$ denote the steady state labor allocation to manufacturing and research, respectively. For a constant flow of effective emissions $\varphi L_Y^{SS}$ this equation leads to a constant level of environmental quality $N^{SS}=\bar{N}-\frac{\varphi }{1-\delta } L_Y^{SS}$. Technologically-advanced societies allocate a larger share of their scarce resources to R&D (i.e. relatively higher labor $L_S^{SS}$) which leads to higher growth and productivity in the economy’s final good production, and lower emissions intensity. Thus, investing in new and better technologies is key to sustainable development. Importantly, this requires households with long-term orientation who supply liquidity to the intermediate firms that perform R&D. We now turn to the problem of households.

2.3 Households

Following Fig. 3 and our discussion in the Introduction, environmental quality is positively correlated with households’ long-term orientation, and affects their investment decisions. Therefore, we consider an endogenous intertemporal discount rate $\rho (N)>0$ (rate of impatience), that depends on the quality of the natural environment N, with $\rho '(N)<0, \rho ''(N)>0$. Households own the assets in this economy, K, have logarithmic preferences and supply their constant labor unit L inelastically to manufacturing and R&D, i.e., $L=L_Y+L_S$. Their optimization is standard and reads:

$$\begin{aligned} \max _{\{C_t\}^{\infty }_{t=0}} \int _0^{\infty } \log (C_t) e^{-\int _0^t \rho (N_s) ds}dt, \end{aligned}$$

subject to the dynamic budget constraint $\dot{K}=r K + w L - C$. Their intertemporal problem leads to the familiar Keynes-Ramsey rule:

$$\begin{aligned} \frac{\dot{C_t}}{C_t}=r_t-\rho (N_t). \end{aligned}$$

(10)

In equilibrium $K=V$, that is households hold the equity in intermediate firms.

Equation (10) shows that consumption growth is positive if the market return to investing in intermediate firms (and thus in innovation) r is higher than the subjective discount rate $\rho (\cdot )$. In that case agents are willing to sacrifice current consumption in order to attain higher consumption in the future. Assume two economies with different environmental qualities $N_{low}$ and $N_{high}>N_{low}$. Ceteris paribus, the economy with $N_{low}$ will be characterized by higher $\rho$, higher consumption, and, according to (10), lower growth. If the economic development of this country is not sufficient to provide a high enough market compensation (through r), households will find it worthwhile to consume now rather than save and invest for the future. In our model this translates to lower investment in intermediate firms (source of growth), which in turn implies manufacturing with low levels of technology, which is polluting. This further worsens development prospects and leads to a vicious cycle of low growth and low environmental quality (environmental and economic poverty trap). We provide detailed intuition below where we analyze the general equilibrium of our economy.

2.4 Equilibrium and Balanced Growth

In equilibrium the return to household assets in Eq. (10), matches the return from investing in intermediate firms (8). Accordingly, substituting r from (10) in Eq. (8) above, with $\dot{C}/C=\dot{Y}/Y=\dot{Q}/Q+\dot{L}_Y/L_Y$, from $Y=Q L_Y$, yields the law of motion for labor allocation:

$$\begin{aligned} \frac{\dot{L}_{Yt}}{L_{Yt}}= \beta A L_{Yt} -\rho (N_t). \end{aligned}$$

(11)

Equations (9′) and (11) describe the dynamic evolution of the economy in the $\{L_Y, N\}$-space. Let hats denote growth rates, i.e., $\hat{Q}=\dot{Q}/Q$. We then have the following definition of a balanced growth equilibrium.

Definition 1

A balanced growth path (BGP)—or balanced growth equilibrium—is characterized by a state where consumption (C), final good production (Y) and technological quality (Q) grow endogenously at a constant rate g, i.e., $\hat{C}=\hat{Y}=\hat{Q} = g$, while labor allocation and environmental quality are in steady state $\{L_Y^{SS}, N^{SS}\}$, on which $\dot{L}_Y=\dot{N}=0$.

We get using (4), (10), and (11), that on the BGP the interest rate is also constant, i.e., $r(N^{SS})=AL-\frac{1-\beta }{\beta } \rho (N^{SS})$; the equilibrium rate of economic growth follows from (10):

$$\begin{aligned} g=AL -\frac{1}{\beta }\rho (N^{SS}) \equiv g(N^{SS}). \end{aligned}$$

(12)

Other things equal, economic growth responds positively to an increase in the productivity parameter of the growth engine A. However, this first order (static) effect can be mitigated–or even reversed–depending on the long-term orientation of households. If the additional income from productivity increases results in subsequently increasing consumption relatively more than investing in innovation, this second order (dynamic) effect can worsen the environmental quality and increase the intertemporal rate of discount, thus reducing growth prospects in the long run.

Moreover, following the properties of $\rho (\cdot )$, the long-run growth rate in (12) is an increasing and concave function in N, i.e., $g'(\cdot )>0, g''(\cdot )<0$. We show below that there are two stable balanced growth equilibria: an equilibrium with high environmental quality and growth and one with low environmental quality and growth. Furthermore, in accord with the empirical facts documented in the introduction, for countries in the low equilibrium with high rates of intertemporal discounting, short-term income increases through exogenous technological improvements in the economy’s growth engine (R&D) can further worsen both their environmental and economic situation.

3 Multiple Equilibria and the Process of Development

3.1 Parametric Assumptions and Multiple Equilibria

All along the BGP $\dot{L}_Y=\dot{N}=0$. From (9′) and (11), the steady state level of environmental quality $N^{SS}$ is given by the solution to:

$$\begin{aligned} \frac{\rho (N^{SS})}{\beta A}= \frac{ 1-\delta }{\varphi }(\bar{N}-N^{SS}), \end{aligned}$$

(13)

while the steady level of economic growth comes from (12). For a well defined problem we impose the following parametric assumptions:

Assumption 1

For extreme environmental degradation $N=0$ the intertemporal discount rate obeys $\rho (0) \ge \beta A \frac{1-\delta }{\varphi }\bar{N}$.

Assumption 2

For a certain level of environmental quality $N^* \in [0, \bar{N}]$ that solves $\rho '(N^*)/\beta A =-(1-\delta )/\varphi$, the elasticity of time preference with respect to environment, i.e., $\epsilon _{\rho N} \equiv d\ln \rho /d\ln N$, evaluated at $N^*$, obeys: $\epsilon _{\rho N}^* < - (\frac{\bar{N}}{N^*}-1)^{-1}$.

From (13), the first assumption excludes the possibility of an equilibrium where $N<0$. The second, that comes from the condition $\frac{\rho (N^*)}{\beta A} <\frac{1-\delta }{\varphi }(\bar{N}-N^*)$, sets a sufficient parametric condition that ensures existence and rules out the knife-edge tangency equilibrium. The following proposition establishes the multiplicity of equilibria.

Proposition 1 (Multiplicity)

Let Assumptions 1 and 2 hold. Then, there are two interior balanced growth equilibria that solve (13): one with low environmental quality and low growth–for which $N^{SS}<N^*$; one with high environmental quality and high growth–for which $N^{SS}>N^*$.

Proof

Equation (13) provides the equilibrium of the economy. The LHS function, $\rho (N)/\beta A$, is decreasing and convex ($\rho '(N)<0, \rho ''(N)>0$). With Assumption 1, it starts and ends above the RHS of (13), which is $(1-\delta )/\varphi (\bar{N}-N)$. Accordingly, we have the possibility of three cases: none, one (tangency), or two equilibria. Under Assumption 2, there exists $N^*\in [0,\bar{N}]$ that solves $\rho '(N^*)/\beta A=-(1-\delta )/\varphi$ such that at $N^*$ the LHS of (13) is below the RHS, thus, exactly two equilibria exist $\{N^{SS}_1,N^{SS}_2\}$. With Assumption 2 it holds that $N^{SS}_1<N^*<N^{SS}_2$. Using Eq. (12) and the properties of $\rho (\cdot )$, we also get that $g(N^{SS}_1)<g(N^{SS}_2)$. $\square$

Proposition 1 shows that in an economy with endogenous time preference in environmental quality, two long-run equilibria arise: one with low level of environmental quality and growth (low equilibrium), and one with high level of environmental quality growth (high equilibrium). Figure 4 illustrates the existence and multiplicity of the equilibria.¹⁴ In Proposition 2 below we analyze the stability properties of these equilibria along with the dynamic mechanisms that lead towards them.

3.2 Stability Analysis

This section deals with the stability of the multiple equilibria. The determinant $\Delta$ of the Jacobian of the dynamic system of Eqs. (9′) and (11) evaluated at a steady state $N^{SS}$ reads:

$$\begin{aligned} \Delta = -\varphi L_Y^{SS} \rho '(N^{SS})\left( 1-\frac{\rho '(N^*)}{\rho '(N^{SS})}\right) , \end{aligned}$$

(14)

with $\rho '(N^*)=-\beta A (1-\delta )/\varphi$ from Assumption 2 above. Using our assumptions on $\rho$ we have three cases for $\Delta$:

• 1. For $N^{SS}<N^* \rightarrow \rho ' (N^*)/ \rho '(N^{SS})<1$, which implies $\Delta >0$,

• 2. For $N^{SS}>N^* \rightarrow \rho ' (N^*)/ \rho '(N^{SS})>1$, which implies $\Delta <0$,

• 3. For $N^{SS}=N^* \rightarrow \rho ' (N^*)/ \rho '(N^{SS})=1$, which implies $\Delta =0$.

Case 3 is excluded by Assumption 2. The proposition below deals with the stability of the multiple equilibria established before.

Proposition 2 (Stability)

(i) The high equilibrium ($N^{SS}>N^*$) is always stable with saddle path type of stability. (ii) The low equilibrium ($N^{SS}<N^*$) is stable if $\beta A L_Y^{SS}<1-\delta$; the type of stability is either an attractive focus or an attractor.

Proof

The first part comes directly from Case 2 above with $\Delta <0$. For the second part substitute $\rho (N^{SS})=\beta A L_Y^{SS}$ from (11) in the trace of the Jacobian $2 \beta A L_Y^{SS}-\rho (N^{SS})-(1-\delta )$ to get that the trace reads as $\beta A L_Y^{SS}-(1-\delta )$. A sufficient condition for a stable equilibrium arises from Case 1 ($\Delta >0$) and from the fact that the trace is negative for $\beta A L_Y^{SS}<1-\delta$.

$\square$

The proposition above establishes that the multiple equilibria of economic development are stable equilibria. The high growth equilibrium is saddle-path stable as in such a case growth through innovation favours environmental quality. However, in the low growth economy, growing though low R&D activity suppresses environmental quality. Condition $\beta AL_Y^{SS}<1-\delta$ rules out the possibility of an unstable low growth equilibrium, in other words, this condition sets the bounds to growth in an economy with low technological quality. Interestingly, following the discussion on the vicious cycle described in the previous section, this condition shows that the polluting effect of productivity from higher growth through lower quality manufacturing ($\beta A L_Y^{SS}$) shall be sufficiently lower than the speed of regeneration of the natural environment ($1-\delta$). This finding is consistent with empirical evidence where economies in a development trap exhibit very low but stable non-zero long-run growth and level of environmental quality (see Fig. 2).

Below we discuss the dynamics of the economy under study and show that income increases, stemming from positive productivity shocks in innovation, benefit only the equilibrium with $N^{SS}>N^*$ (high equilibrium), while they can further worsen the prospects of economies with $N^{SS}<N^*$ (low equilibrium).

3.3 Dynamics and Comparative Development

We now investigate the effect of exogenous technological improvements (e.g. through international technology transfers, foreign aid or imitation) on the equilibrium rate of economic growth and level of environmental quality. Let $\epsilon _{NA}^{SS} \equiv d\ln N^{SS} /d\ln A$ measure the relative change in the steady state level of environmental quality following a relative increase in productivity of the economy’s growth engine, and $\epsilon _{\rho N}^{SS}$ denote the elasticity $\epsilon _{\rho N}$ defined in Assumption 2 above, evaluated at the steady state.

Proposition 3 (Technological improvements)

(i) An increase in productivity A improves at the same time the equilibrium level of environmental quality and economic growth in the high equilibrium ($N^{SS}>N^*$). (ii) In the low equilibrium ($N^{SS}<N^*$) it unambiguously worsens environmental quality; it also worsens growth prospects when $\rho (N^{SS}) \epsilon _{\rho N}^{SS} \epsilon _{NA}^{SS}>\beta A L$.

Proof

Totally differentiating Eq. (12), the relative change in equilibrium growth $\tilde{g}\equiv dg/g$ following a relative increase in productivity $\tilde{A} \equiv dA/A>0$ reads:

$$\begin{aligned} \tilde{g}=\frac{1}{g}\left( AL-\frac{1}{\beta }\rho (N^{SS}) \epsilon _{\rho N}^{SS} \epsilon _{NA}^{SS}\right) \tilde{A}, \end{aligned}$$

(15)

From manipulating (13) with $N^{SS}=N^{SS}(A)$ we get that:

$$\begin{aligned} \epsilon _{\rho N}^{SS} \epsilon _{NA}^{SS}\left( 1-\frac{\rho '(N^*)}{\rho '(N^{SS})}\right) =1. \end{aligned}$$

(16)

Since $\epsilon _{\rho N}^{SS}<0$, the sign of $\epsilon _{NA}^{SS}$ for the above to hold and following our assumptions on $\rho$ proves the proposition. We showed in Case 2 of section 3.2 that $\rho ' (N^*)/ \rho '(N^{SS})>1$ for $N^{SS}>N^*$, such that $\epsilon _{NA}^{SS}>0$ and thus from (15) $\tilde{g}>0$. For $N^{SS}< N^*$ we always get $\epsilon _{NA}^{SS}<0$, while $\tilde{g}<0$ when $\rho (N^{SS}) \epsilon _{\rho N}^{SS} \epsilon _{NA}^{SS} > \beta AL$. $\square$

Technological improvements are key to sustainable development. However, the literature seems to agree on the fact that when these occur exogenously, through aid or technology transfer, these are not always sufficient to help countries escape the environment-poverty trap. Yet there is no consensus on the mechanisms behind this fact. Proposition 3 shows that endowments of environmental quality play a crucial role for the effectiveness of development policies, when environmental quality works through the subjective discount rate of individuals.

Importantly, Proposition 3 highlights the interplay between long-term orientation, environmental quality, and growth through innovation, and matches the stylized facts of Figs. 1 and 2. An exogenous increase in A has a first-order effect on household budget by increasing the income of individuals through the return on equity, $r(N^{SS})=AL-\frac{1-\beta }{\beta } \rho (N^{SS})$. Societies with very good environmental quality, exhibit higher patience (low $\rho$) and thus can reap the benefits of such a productivity increase to further invest in R&D that advances both their economic and environmental situation. On the other end of the spectrum, societies with poor environmental quality are oriented towards the short-term (high $\rho$). Provided that their $\rho$ is high and their productivity level A is already low, a productivity increase would trigger relatively more consumption rather than investment, thus worsening both their economic and environmental development prospects.

Further intuition about our mechanism can be gained by visualizing the dynamic behaviour of the economy in Figs. 4 and 5. The following phase diagram of Fig. 4 depicts the dynamics of the economy in the $\{L_Y, N\}$-space. For a given productivity level A there are two equilibria: the high equilibrium with high level of environmental quality and innovation (high labor in R&D, $L_S$, and thus low in manufacturing, $L_Y$), steady state $SS_H$, and the low equilibrium with low environmental quality and innovation, $SS_L$. Equilibrium $SS_H$ is saddle stable as we already established; the figure also depicts its stable arm. For the chosen parameter values,¹⁵ equilibrium $SS_L$ is an attractor locally (two real and negative eigenvalues of the Jacobian matrix evaluated at $SS_L$). Studying the phase diagram, we also see that an increase in the productivity parameter to a level $A'>A$ improves the situation in the good equilibrium ($SS'_H$) while it worsens, both, environmental and growth prospects for economies in the low equilibrium ($SS'_L$); the dynamic evolution depending on the initial equilibrium is depicted by the red dots.

Figure 5 shows the dynamics of two economies, one in the high and one in the low equilibrium, when productivity increases at $t=50$. For both economies (a, high) and (b, low), the first graph shows the scientific labor force $L_S=L-L_Y$, the second the level of environmental quality N, the third the rate of economic growth, i.e., $\hat{C}=\hat{Y}=\hat{Q} + \hat{L}_Y=A L_S +\beta A L_Y-\rho (N)$—from Eqs. (4) and (11), and the fourth the evolution of manufacturing Y (production at $t=0$ is normalized to unity for comparison purposes). Following our previous discussion, and focusing on panel (b)—the low equilibrium, an exogenous productivity increase in R&D activity eventually worsens development and environmental prospects: with short-sighted agents (due to poor local environment), the short-run growth spell (bottom left) leads to an ephemeral increase in demand for low quality manufacturing which is polluting, thus lowering patience and investment in innovation. This reinforces the vicious cycle of lower environmental quality and lower growth in the long-run. The opposite holds true for economies in the high equilibrium panel (a) that direct any productivity increases into long-term oriented investments in innovation.

Our results are also in line with Figs. 1 and 2 where for economies that lie above a threshold level of environmental quality, R&D spending is higher, the level of patience is higher and the level of environmental quality is higher.

Fig. 4

Phase diagram $\{L_Y,N\}$. Dashed line is for $A'>A$. Steady states $SS_H$ (high) and $SS_L$ (low) correspond to A, while $SS'_H$ and $SS'_L$ to $A'>A$. The high equilibrium is saddle stable; the low equilibrium is an attractor. The continuous arrow lines show the stable arms for $SS_H$ and $SS'_H$

Fig. 5

Productivity increase dynamics. Starting at the high steady state, a small technological increase ($A \rightarrow A'>A$) at $t=50$ improves development prospect; starting at the low steady state, it eventually worsens development prospects. During transition from the low equilibrium, the economy experiences only a short-term growth spell that eventually leads to lower growth and output; the dashed line shows the development path before productivity increases

4 Concluding Remarks

We contribute to the environment-poverty nexus a new mechanism that builds on the joint relation between long-term orientation, environmental quality and innovation. Based on empirical evidence, we assume a negative relationship between the subjective discount rate and environmental quality in an endogenous growth model with local pollution externalities. We argue that investing in technologically-advanced production methods is key to sustainable development: it leads to higher efficiency of production and preserves the local ecosystem. However, this presupposes that households’ long-term views are not distorted by the poor natural environment they live in.

In line with empirical observations, in this setup two equilibria arise: one with low environmental quality and poor economic development, and one with high environmental quality and good economic development. It is also well documented that exogenous technological improvements do not help societies escape the low equilibrium, while benefit those with good sustainability scores, which is also captured by our model.

The usual recommendation to help populations out of environment-poverty traps is direct foreign aid to either facilitate migration out of fragile environments or investment in improving the living conditions of the remaining ones (World Bank 2008). In our framework short-term income increases through aid or technology transfer, may not be enough to help countries escape an environment-poverty trap under a threshold level of environmental quality. We show that investment choices of individuals towards clean R&D technologies under productivity increases can mitigate the adverse effects of economic activity on the natural environment and, in turn, generate a double dividend of higher growth and better environmental quality. This is possible only if individuals are long-term oriented so as to sacrifice ephemeral pleasure for environmental and economic gains in the future. Therefore, our model highlights the possibility of promoting the economic and the environmental dimension of sustainability with complementary policies that protect the natural environment and influence long-term views. Policy options vary from educational programs that target long-term orientation, environmental sustainability and innovation, to incentive structures towards long-term choices such as taxing consumption with revenue recycling promoting innovation, and/or restoration of ecosystem services.

Appendices

Appendix A: Regression Results of Figs. 1 and 2

See Tables 1 and 2.

Table 1 OLS regression results Fig. 1

Table 2 OLS regression results Fig. 2

Appendix B: Emissions Intensity

In this Appendix we provide further empirical evidence that supports our assumption on the inverse relation between emissions intensity of production and the technology level of the economy, i.e., $\phi '(Q)<0$, $\phi ''(Q)>0$, and on the specific functional form $\phi =\varphi Q^{-1}$, needed to ensure a balanced growth path in the model.

In equilibrium, for a constant flow of emissions $E= \phi (Q) Y$, Eq. (9′) leads to a constant level of environmental quality $N=\bar{N}-\frac{\phi (Q)}{1-\delta } Y$, such that $\frac{\phi (Q)}{1-\delta } = \frac{\bar{N}-N}{Y}$. To visualize $\frac{\bar{N}-N}{Y}$ against the level of technology Q for each of the 133 countries in our sample, we proxy, as in Fig. 1, Q by R&D expenditure (% GDP), environmental quality N by the environmental performance index (EPI, in percentage terms) and $\bar{N}$ by its maximum value i.e., $\bar{N}=100\%=1$; for Y we use GDP from World Bank Indicators (in constant PPP 2017 international trillion $).

Figure 6 below shows (in logarithmic scale) a clear negative relationship between $\frac{\phi (\cdot )}{1-\delta } = \frac{\bar{N}-N}{Y}$ and Q (as proxied by R&D expenditure) that confirms the properties $\phi '(Q)<0$, $\phi ''(Q)>0$. The best fit to the data yields $\frac{\phi (Q)}{1-\delta }= 0.972 Q^{-0.95}$ (solid line), which justifies our assumption on the inversely proportional functional form $\phi (Q) = \varphi Q^{-1}$. From the above we also get $\varphi \approx (1-\delta )0.972$.

Fig. 6

Emissions intensity $\phi (Q)$ (logarithmic scale). Using Eq. (9′) in equilibrium the graph plots the term $\frac{\phi (\cdot )}{1-\delta }=\frac{\bar{N}-N}{Y}$ against R&D expenditure (%GDP)—as a proxy for the level of country-specific technology Q. We proxy N by the EPI (in percentage terms)—with $\bar{N}=1$, and Y by GDP in PPP 2017 international trillion$. The solid line gives the best fit to the data. Sources: EPI Score, EPI (2018); R&D expenditure and GDP by World Bank Indicators

Appendix C: Choice of Parameters

This part of the Appendix discusses our parameter choice for Figs. 4 and 5. Since there is no population growth we normalize $L=1$. For the steady states that solve (13), we need to establish parameters $\beta$ and $\bar{N}$, the ratio $\frac{1-\delta }{\phi }$, the functional form of $\rho (N)$ and A. From $C=(1-\beta ^2)Y$ we set $\beta =0.5$ such that $C/Y=0.75$, a standard value in the literature. From Appendix B we set $\bar{N}=1$ and $\frac{1-\delta }{\phi }=\frac{1}{0.972}=1.029$, while we choose $\delta =0.9$ as in Angelopoulos et al. (2013). With regards to the functional form of $\rho (N)$ we assume, similar to Strulik (2012) and as in Dioikitopoulos et al. (2020), that $\rho (N)=\rho _0 \exp (-\eta N)$, with $\rho _0,\eta >0$. To compare one economy in the low with one in the high equilibrium, we choose parameters $A, \rho _0$ and $\eta$ that lead to a low equilibrium with environmental quality below the threshold $N^*=56$ (see Figs. 1 and 2), and to a high equilibrium with environmental quality above that threshold; in addition for the low equilibrium we aim at a consumption growth rate of $g_{low}=0.02$, and $g_{high}=0.03$ for the high equilibrium (from Eq. 12). The above are satisfied by $A=0.05$, $\rho _0=0.04$ and $\eta =2.3$, while as a productivity shock we choose a $10\%$ increase in productivity, i.e., $A^{\prime }=0.055$.