Public Debt, Life Expectancy, and the Environment

Abstract

The economic literature has shown that some countries may be trapped in what is called an ”environmental poverty trap”: poor longevity implies little maintenance of the environment, which leads to high levels of pollution that in turn keeps life expectancy low. Since life expectancy is an important determinant of saving, these economies may not be able to grow. This article aims to provide policy recommendations to improve both environmental quality and growth in the context of debt consolidation. Notably, it studies how public debt and public maintenance may be used to escape from the environmental poverty trap. A welfare analysis is then undertaken to show that public debt is an instrument which helps to solve the capital over-accumulation problem and to achieve environmental objectives.

Appendices

Appendix : A: Stylized fact: A negative correlation between public debt and the environmental quality

The correlation coefficient between the mean of the Net General Government Debt ratio and the mean of the EPI over the 2000-2010 period is −0.161. It is significant at the 1 percent level. The correlation is performed on a sample of 59 countries (see Table 2 (Fig. 2)) .

Fig. 2

Correlation between Net General Government Debt and the EPI

Table 2 List of countries (2000-2010)

The EPI data come from the Yale Center for Environmental Law and Policy [13]. The Net General Government Debt data come from the IMF World Economic Outlook database [14].

Appendix : B: Dynamics when

$\mathbf { \underline {e_{1}} \le \,J\,\le \, \underline {e_{2}} }$ As explained in Section 5, the present phase diagram is one of a wide range of possibilities. Indeed, our relative steady states may vary a little given the position of the curves. In fact, $\overline {e}_{1}$ may be higher than $\underline {e_{2}}$. That possibility does not change the policy recommendation because these points only represent the environmental trap’s situation. It may only improve or reduce the probability of falling into the trap when we give values are given to parameters.

Depending on where the J threshold is placed, the dynamics may vary somewhat. Section 5 presents the case in which there are three areas of convergence. If we decided to improve medical knowledge (i.e., impose a lower J), there are thus have two convergence areas. Indeed, the point $(\underline {k_{2}},\underline {e_{2}})$ is no longer an attraction point because ${\underline {e_{2}}}>J$. The convergence area toward the high equilibrium is thus larger. This is represented in Fig. 3.

Fig. 3

Dynamics when $\underline {e_{1}} \le \,J\,\le \, \underline {e_{2}}$

It is also possible to look at the extreme case. If medical knowledge is very high, $J<\overline {e_{1}}$, the curves that prevail for the analysis of dynamics are in red. If medical knowledge is very low, $J>\overline {e_{2}}$, the curves that prevail are in green.

Nevertheless, failing to present an

Appendix C: Proof of proposition 1

1.1 Variation of dk with Respect to db

$$\begin{array}{@{}rcl@{}} R\pi\gamma\sigma(1-\epsilon k^{\epsilon-1})-P\left[\frac{\sigma(1+\pi)}{\pi(1-\gamma)}-\sigma+\sigma\epsilon k^{\epsilon-1}\right] & = & (1-\eta)\pi\gamma\sigma(1-\epsilon k^{\epsilon-1})\\ & & -(1+\pi+\pi\gamma\eta-\pi\gamma)\left[\frac{\sigma(1+\pi)}{\pi(1-\gamma)}-\sigma+\sigma\epsilon k^{\epsilon-1}\right]\\ & = & (1+\pi)\sigma(1-\epsilon k^{\epsilon-1})-(1+\pi+\pi\gamma\eta-\pi\gamma)\frac{\sigma(1+\pi)}{\pi(1-\gamma)} \end{array} $$

This is higher than zero for $k\leq \frac {-1-\pi \gamma \eta }{\pi (1-\gamma )\epsilon }<0$, which is impossible. This expression is thus always negative. Given the sign of the determinant, we obtain the signs that we put in the corresponding cases in Table ??

1.2 Variation of dk with Respect to dg

$$\begin{array}{@{}rcl@{}} R\pi\gamma(\rho-\sigma)+P(\rho-\sigma) & = & (1-\eta)\pi\gamma(\rho-\sigma)\\ &&+(1+\pi+\pi\gamma\eta-\pi\gamma)(\rho-\sigma)\\ & = & (1+\pi)(\rho-\sigma) \end{array} $$

Given assumption 1, this is always positive. Given the sign of the determinant, the signs that are put in the corresponding cases in Table 1 are obtained.Variation of de with Respect to db

$$\begin{array}{@{}rcl@{}} -Q\pi\gamma\sigma(1-\epsilon k^{\epsilon-1})+O\left( \frac{\sigma(1+\pi)}{\pi(1-\gamma)}-\sigma(1-\epsilon k^{\epsilon-1})\right)=\pi\gamma\sigma(1-\epsilon k^{\epsilon-1})\\ \times\left[\frac{\sigma(1+\pi)}{\pi(1-\gamma)}-\sigma(1-\epsilon)\epsilon k^{\epsilon-1}-\sigma\epsilon(1-\epsilon)bk^{\epsilon-2}+\beta\epsilon k^{\epsilon-1}\right]\\ +\left[\frac{\sigma(1+\pi)}{\pi(1-\gamma)}-\sigma(1-\epsilon k^{\epsilon-1})\right]\\ \times\left[-\pi\gamma\sigma(1-\epsilon)\epsilon k^{\epsilon-1}-\pi\gamma\sigma(1-\epsilon)\epsilon bk^{\epsilon-2}+\pi\gamma\beta\epsilon k^{\epsilon-1}\right]\\ =+\frac{\sigma(1+\pi)}{{\pi}(1-\gamma)}\left[\sigma\pi\gamma(1-\epsilon k^{\epsilon-1})-\pi\gamma\sigma(1-\epsilon)\epsilon k^{\epsilon-1}-\pi\gamma\sigma(1-\epsilon)\epsilon bk^{\epsilon-2}+\pi\gamma\beta\epsilon k^{\epsilon-1}\right] \end{array} $$

This is higher than 0 if:

$$\begin{array}{@{}rcl@{}} \sigma-\sigma\epsilon k^{\epsilon-1}-\sigma(1-\epsilon)\epsilon k^{\epsilon-1}-\sigma(1-\epsilon)\epsilon bk^{\epsilon-2}+\beta\epsilon k^{\epsilon-1} & > & 0\\ \sigma k^{1-\epsilon}-2\sigma\epsilon+\sigma\epsilon^{2}-\sigma\epsilon\frac{b}{k}+\sigma\epsilon^{2}\frac{b}{k}+\beta\epsilon & > & 0 \end{array} $$

Thus, it can easily be confirmed that the sign will crucially depend on the $\frac {b}{k}$ level.Variation of de with Respect to dg

$$\begin{array}{@{}rcl@{}} Q\pi\gamma(\sigma-\rho)+O(\sigma-\rho) & = & \pi\gamma(\sigma-\rho)\left[\sigma(1-\epsilon)\epsilon k^{\epsilon-1}+\sigma\epsilon k^{\epsilon-2}(1-\epsilon)b-\frac{\sigma(1+\pi)}{\pi(1-\gamma)}-\beta\epsilon k^{\epsilon-1}\right]\\ & & +(\sigma-\rho)\left[\pi\gamma\epsilon\beta k^{\epsilon-1}-\pi\gamma(1-\epsilon)\epsilon b\sigma k^{\epsilon-1}-\pi\gamma\sigma(1-\epsilon)\epsilon k^{\epsilon-1}\right]\\ & = & -\frac{\sigma(1+\pi)\pi\gamma(\sigma-\rho)}{\pi(1-\gamma)}\\ & = & \frac{\sigma(1+\pi)\gamma(\rho-\sigma)}{1-\gamma} \end{array} $$

Given assumption 1, this is always positive. Given the sign of the determinant, the signs are obtained that are put in the corresponding cases in Table 1.