2.1 EKC hypothesis

The EKC hypothesis was first explained by the combination of three types of effects that occur in the development process: (i) the production scale effect, which means that the increase in production is accompanied by pollution; (ii) the composition effect, which takes into account the pollution intensity levels of different industries, and (iii) the technological effect, which describes technology changes in the production process (Grossman and Krueger, Reference Grossman and Krueger1991, Reference Grossman and Krueger1995; Panayotou, Reference Panayotou1993). Theoretical models then began to be developed. According to de Bruyn and Heintz (Reference de Bruyn, Heintz and van den Bergh2002) and Kijima et al. (Reference Kijima, Nishide and Ohyama2010), the theoretical mechanisms underlying these models are based on three factors: changes in behavior and preferences, institutional changes, and technological and organizational changes.

In the case of deforestation, the theoretical explanation of the EKC is provided by López (Reference López1994). He considers an economy with two sectors: a primary sector that uses natural resources as a factor of production, and the rest of the economy that uses other factors. The primary sector is characterized by agriculture whose production is dependent not only on the cultivated land area (the level of deforestation) but also on the forest stock ensuring quality and soil fertility. He found that when the effects of stock of forest resources on agricultural production are internalized, the economic growth in developing countries will be accompanied by low deforestation along the trajectory of the inverted U-shape. A number of empirical studies have attempted to validate or invalidate the Kuznets relationship between different indicators of environmental degradation and income in the last two decades. In general, the mixed results are due either to the type of environmental indicators used in the country or the group of countries studied; the explanatory variables used; the period of time considered; and econometric techniques used (Bhattarai and Hammig, Reference Bhattarai and Hammig2001).

The first empirical studies on deforestation began in the 1990s with the studies of Cropper and Griffiths (Reference Cropper and Griffiths1994), Shafik (Reference Shafik1994) and Koop and Tole (Reference Koop and Tole1999). The findings of these studies are different despite their having used the same quadratic model. But these findings may be explained by differences in sample and study period. Indeed, Cropper and Griffiths (Reference Cropper and Griffiths1994), based on panel data from 64 countries from 1961 to 1988, found that the EKC is verified in Africa and Latin America but not in Asia. Koop and Tole (Reference Koop and Tole1999), however, show that the EKC only exists in the countries of Latin America when using panel data from 76 tropical developing countries from 1961 to 1992. In contrast, Shafik (Reference Shafik1994) finds no evidence of the existence of the EKC from a sample of 66 countries over the period 1962–1988.

Apart from the differences in the samples, studies during the first decade did not take into account institutional factors in their analysis. Yet institutional development plays an important role in the environmental degradation and economic growth relationship. Indeed, institutional factors affect the EKC relationship, especially in low-income countries. For example, the level of education, political freedoms and civil rights can help to improve the quality of the environment (Torras and Boyce, Reference Torras and Boyce1998). Similarly, the quality of public policies such as security of property rights or better enforcement of contracts can help flatten the EKC and reduce the environmental cost of economic growth (Panayotou, Reference Panayotou1997).

This gap was filled by the research work during the second decade whose major difference was a focus on institutional indicators. Thus, Bhattarai and Hammig (Reference Bhattarai and Hammig2001), by incorporating institutional variables, confirm the EKC relationship for 66 countries in Latin America and Africa but find no evidence in Asia from 1971 to 1991. They also show that institutional indicators (political rights and civil liberties) significantly reduce deforestation. Similarly, Ehrhardt-Martinez et al. (Reference Ehrhardt-Martinez, Crenshaw and Jenkins2002) show the existence of an EKC with a threshold of US$1,150 in 74 least-developed countries over the period 1980–1995. They also find a negative effect of the strengthening of democracy on deforestation. Culas (Reference Culas2007), using the quality indicators of environmental policy such as the implementation capacity of the contracts and the efficiency of the bureaucracy, finds an EKC relationship for deforestation only for Latin American countries. He confirms the positive effect of improving institutional policies on reducing deforestation over the period 1972–1994.

However, some studies have rejected the existence of the EKC despite controlling institutional factors. In particular, Barbier (Reference Barbier2004), in contrast to previous studies, used as the dependent variable the expansion of agricultural land which is a proxy for deforestation. Using a quadratic model, he finds no evidence of the existence of the EKC in samples from Latin America, Asia and Africa over the period 1961–1994. Concerning institutional variables, Barbier shows that corruption control reduces the expansion of agricultural land and thus negatively affects deforestation. Similarly, Arcand et al. (Reference Arcand, Guillaumont and Jeanneney2008) developed a theoretical model focusing on the factors affecting the incentives to transform the forested land into agricultural land. By testing these theoretical hypotheses on a sample of 101 countries from 1961 to 1988, they find that the EKC is not valid. However the authors show that stronger institutions reduce deforestation.

Furthermore, other studies have questioned the supposed parametric form of the relationship between deforestation and income. The purpose of this work is to explore a possible nonlinearity in the process of deforestation. Thus, Azomahou and Van (Reference Azomahou and Van2007), from a nonparametric approach, reject the EKC relationship between income and deforestation for 59 developing countries. However, they find the same results on the institutions, while Chiu (Reference Chiu2012), using a threshold effect panel model, shows that the EKC is verified for 52 developing countries during the period 1972–2003. This approach allows him to determine the endogenous turning point as between US$2,459–3,021.

2.2 Convergence hypothesis

The convergence hypothesis is a new approach to understanding the relationship between the environment and economic growth. This hypothesis was theoretically enhanced by the work of Brock and Taylor (Reference Brock and Taylor2010) based on the stylized facts. These authors were inspired by Solow's (Reference Solow1956) growth model and support the idea that the forces of diminishing returns and technical progress, identified by Solow as being fundamental to the growth process, may also be in the growth–environment relationship. Thus, Brock and Taylor (Reference Brock and Taylor2010) extend the Solow model by assuming that production generates pollution and a constant share of production is allocated to clean-up activities through technical change abatement.

Results show that countries converge in terms of emissions. In other words, emissions increase initially in poor countries because of their rapid growth, but they decrease later when growth slows (due to the forces of convergence to the developed countries' stationary state). These results imply that the mechanism that governs emissions is the decline in production growth rate that is induced by convergence forces combined with the constant rate of technical progress in the abatement of pollution. However, Stefanski (Reference Stefanski2013) shows that the emissions path of developing countries can also be determined by changes in the growth rate of the emission intensity due to structural changes in these economies.

Moreover, Ordas Criado et al. (Reference Ordas Criado, Valente and Stengos2011), using a neoclassical growth model with endogenous emission reduction, have predicted a beta-convergence in pollution. However, unlike Brock and Taylor (Reference Brock and Taylor2010), they assume that both the saving rate and the propensity to spend on abatement are endogenously determined by utility maximization. Also, their framework is considered to be a flow-pollution model in which emission-reducing investment is excluded and a clean-technologies model where abatement is optimized without capital accumulation. This allows them to derive the joint dynamics relationship between pollution growth, pollution levels, and income growth rates, which can be tested using regression methods.

In the case of deforestation, it is a convergence in terms of deforestation which is consistent with the forest transition hypothesis (Mather, Reference Mather1992). According to Mather, forest cover tends to decrease in countries which are at the beginning of their development and this trend is reversed in developed countries with an increase in forest cover through reforestation. This change in forest cover is what the author called forest transition – that is, the passage from deforestation to reforestation. Nevertheless, according to recent studies, this transition can also be observed in developing countries through the awareness of climate change issues and the implementation of emission reduction instruments caused by deforestation and forest degradation (REDD+). For example, this phenomenon is observed in India, Bangladesh, Costa Rica (Kanninen et al., Reference Kanninen, Murdiyarso, Seymour, Angelsen, Wunder and German2007), China (Xu et al., Reference Xu, Yang, Fox and Yang2007) and Viet Nam (Mather, Reference Mather2007).

In the literature, there are three types of convergence. The first is beta convergence which means that poor countries tend to grow faster (and are therefore more polluting) than rich countries (Sala-i-Martin, Reference Sala-i-Martin1996). Technically, it is indicated by an inverse relationship between the growth of a variable and its initial level (Barro and Sala-i-Martin, Reference Barro and Sala-i-Martin1992). The second, sigma convergence, is defined as a convergence which occurs if the dispersion of the current level of per capita GDP of a group of countries tends to decrease over time (Sala-i-Martin, Reference Sala-i-Martin1996). This implies in the case of pollution or deforestation that countries will have on average approximately the same levels of future emissions or deforestation. The third is stochastic convergence which states that a pair of countries converges stochastically if their differences are stationary emissions (Aldy, Reference Aldy2006).

The convergence hypothesis has been empirically tested by many studies. These tests have largely focused on CO₂ emissions and results differ according to the type of convergence, study sample, and methods used. Thus, Strazicich and List (Reference Strazicich and List2003) show from the tests of both cross-section data regression (beta-convergence) and unit root (stochastic convergence) that 21 industrialized countries converge on CO₂ emissions over the period 1960–1997. Aldy (Reference Aldy2006) confirms these previous results by the sigma-convergence tests for 23 OECD countries, unlike the full sample of 88 countries that diverge on CO₂ emissions per capita over the period 1960–2000. Moreover, Westerlund and Basher (Reference Westerlund and Basher2008), using a unit root test on a panel of 28 countries (developed and developing) covering the period 1870–2002, show that these countries converge in CO₂ emissions. In contrast, over the period 1870–2009, Herrerias (Reference Herrerias2013) finds only a convergence club of CO₂ emissions by energy source for many countries. By empirically testing their theoretical hypothesis of absolute convergence in per capita emissions arising from the Green Solow model, Brock and Taylor (Reference Brock and Taylor2010) find a convergence of CO₂ per capita for 165 developed and developing countries between 1960 and 1998.

Finally, to circumvent econometric weaknesses suffered by the analysis of level variables in the EKC, Stern et al. (Reference Stern, Gerlagh and Burke2017) use an approach in terms of the long-term growth rate of the emissions and income relationship. These econometric weaknesses relate in particular to unit root problems (Wagner, Reference Wagner2008) and indeterminacy of the temporal effect (Vollebergh et al., Reference Vollebergh, Melenberg and Dijkgraaf2009). Stern et al.'s (Reference Stern, Gerlagh and Burke2017) approach allows them to test both the EKC and the beta convergence hypotheses of the Green Solow model. They find an EKC for emissions of both SO₂ and CO₂, which however has a turning point out of sample. The authors also confirm the beta convergence for the two pollutants over the period 1971–2010 on a sample of 134 developed and developing countries.

3.1 Empirical model

The empirical model is inspired by the new approach developed by Stern et al. (Reference Stern, Gerlagh and Burke2017). This approach is based on the long-run growth rate of the environmental degradation indicator and income. The advantage of the long-run growth rate method compared to the traditional approach of analyzing variables as levels is that it allows us first to test several theoretical hypotheses including both the income-environmental degradation elasticity, and the EKC and convergence hypotheses. Then, by taking the average growth rate over a long period of time, it allows us to filter short-run effects and to put more weight on the long-run components of variability. Finally, this approach solves a number of econometric problems such as spurious regression and time effect identification. It is therefore suitable for analyzing the dynamics of the rate of change of forest cover that is assumed to be non-stationary (Polomé and Trotignon, Reference Polomé and Trotignon2016).

The empirical form is given by:

(1)\begin{equation}{\hat{F}_i} = {\alpha _0} + {\alpha _1}{\hat{G}_i} + {\beta _1}{\hat{G}_i}{G_{i0}} + {\beta _2}{F_{i0}} + {\beta _3}{G_{i0}} + X^{\prime}\theta + {\varepsilon _i},{\varepsilon _i} \to iid(0,{\sigma ^2}),\end{equation}

where ${\hat{F}_i}$ is the long-run rate of change of forest cover per capita (called deforestation if this rate is negative) defined by ${\hat{F}_i} = (1/T)({{F_{iT}} - {F_{i0}}} )$ where F_iT and F_{i 0} are the log of the per capita forest area at the end of period T and the early period of country i respectively. ${\hat{G}_i}$ is the long-run growth rate of GDP per capita of country i : ${\hat{G}_i} = (1/T)({{G_{iT}} - {G_{i0}}} )$ where G_iT and G_{i 0} are the log of per capita GDP in the last period and the country's early period respectively. X is a vector of control variables including the agricultural land (as a percentage of land area), the population density (number of people per hectare), the degree of openness, the literacy rate, and institutions (political rights and civil freedoms). These variables are averages over the period studied with the simple cross-country mean deducted.

In equation (1), α ₁ represents income-deforestation elasticity which is expected to be positive in accordance with the IPAT (Impact = Population × Affluence × Technology) hypothesis, and α ₀ is an estimate of the mean of ${\hat{F}_i}$ for countries with zero economic growth, with the others variables being constant. As the sample mean is deducted from each of the continuous levels variables, α ₀ may be interpreted as the mean rate of change in forest cover for a country. β ₁ is the coefficient associated with the interaction variable between the rate of economic growth and the initial level of the log per capita income to test the EKC deforestation hypothesis. The latter is verified if α ₁ > 0 and β ₁ < 0. The EKC turning point can be computed where $\partial \hat{F}/\partial \hat{G} = 0$ as $\tau = exp ({ - ({\alpha_1}/{\beta_1}) + {\mu_G}} )$, where μ_G is the cross-country mean of initial GDP per capita that was deducted from the initial level of the GDP per capita variable prior to estimation. The convergence hypothesis, in turn, holds if β ₂  < 0, that is, there is beta convergence in the level of forest per capita (see Barro and Sala-i-Martin, Reference Barro and Sala-i-Martin1992). Likewise if β ₃ = −β ₂, then there is beta convergence in the initial forest area per dollars $({\tilde{F}_{i0}} = {F_{i0}} - {G_{i0}})$ without an additional effect of the initial level of income on the change in growth rate of forest cover.

Moreover, to capture the impact of the level of income on the time effect, equation (1) is estimated by replacing G_{i 0} with G_i (the log of income per capita averaged over time in each country). Hence, if β ₃  > 0, then forest cover use (or deforestation) declines faster over time, the higher the level of income (holding the others variables constant). This would be consistent with the positive (resp. negative) correlation between forest cover changes (resp. forest cover use) and income per capita.

Following Stern et al. (Reference Stern, Gerlagh and Burke2017), other empirical specifications are tested by applying restrictions to equation (1). These exclusion restrictions are tested using likelihood ratio tests. First, the Ordas Criado et al. (Reference Ordas Criado, Valente and Stengos2011) model is tested by setting β ₁ = 0, which is given as follows:

(2)\begin{equation}{\hat{F}_i} = {\alpha _0} + {\alpha _1}{\hat{G}_i} + {\beta _2}{F_{i0}} + {\beta _3}{G_{i0}} + X^{\prime}\theta + {\varepsilon _i}.\end{equation}

One would expect α ₁  > 0 (in the case of deforestation) and β ₂  < 0. This means that the change in growth rates of forest cover is positively related to output growth (scale effect) and negatively related to forest cover level (called a defensive effect according to Ordas Criado et al. (Reference Ordas Criado, Valente and Stengos2011)).

Second, the short-run Green Solow model (Brock and Taylor, Reference Brock and Taylor2010) is tested by setting ${\alpha _1} = {\beta _1} = {\beta _3} = 0$:

(3)\begin{equation}{\hat{F}_i} = {\alpha _0} + {\beta _2}{F_{i0}} + X^{\prime}\theta + {\varepsilon _i}.\end{equation}

According to Brock and Taylor, the beta-convergence holds if β ₂  < 0.

We also set β ₁ = β ₃ to derive a basic EKC model in growth rates without the initial per capita forest cover and income terms:

(4)\begin{equation}{\hat{F}_i} = {\alpha _0} + {\alpha _1}{\hat{G}_i} + {\beta _1}{\hat{G}_i}{G_{i0}} + X^{\prime}\theta + {\varepsilon _i}.\end{equation}

One would expect α ₁ > 0 and β ₁ < 0 for all negative values of ${\hat{F}_i}$ in the case of deforestation.

Finally, a simple IPAT-inspired growth rates model is tested by setting ${\beta _1} = {\beta _2} = {\beta _3} = 0$:

(5)\begin{equation}{\hat{F}_i} = {\alpha _0} + {\alpha _1}{\hat{G}_i} + X^{\prime}\theta + {\varepsilon _i}.\end{equation}

One would expect α ₁ = 1, consistent with a simple IPAT model which assumes that technology is held constant. Otherwise α ₁ < 1, which would mean that technology influences the rate of economic growth (Ehrlich and Holdren, Reference Ehrlich and Holdren1971).

3.2 Identification strategy

Models are estimated by OLS with the White robust standard error to correct the problem of heteroscedasticity. Indeed, it is likely that the variance of the error term is inversely related to the explanatory variables or related to the effect of the group. This not only because of the fact that the variables of interest (deforestation and GDP per capita) are averages over the sample size, but it can also exist in the sample group (Stern et al., Reference Stern, Gerlagh and Burke2017). The White (Reference White1980), Breusch and Pagan (Reference Breusch and Pagan1979) and Harvey (Reference Harvey1976) tests are used to check all forms of heteroscedasticity. One first uses the White test for the general form of heteroscedasticity. The Breusch-Pagan test is then used for the form in which the model residuals' variance varies with a set of regressors. Finally, it is possible that the residual variance is related multiplicatively with regressors, which leads us to use the Harvey test.

It is also likely that there is an endogeneity problem related to a potential feedback effect of the GDP growth rate and the average GDP level on the rate of deforestation. This feedback goes through agricultural production and forest resources since the agricultural sector and forest resources contribute to income in developing countries. Therefore, deforestation can have an impact on the GDP growth rate. To solve this omitted variable bias, control variables are introduced, such as the level of agricultural production and the degree of openness that influence both the GDP growth rate and the rate of deforestation.

4.1 Description of variables

This study focuses on tropical developing countries which are of interest because deforestation is one of the major environmental problems in these countries (see figure 1). The sample consists of 34 African countries, 21 Latin American countries, 12 Asian countries and 18 European countries (see table Α2 in online appendix 2). The countries were chosen based on the importance of their forest area and its changes. Data on variables cover the period from 1990 to 2010 (for data sources, see table A1 in online appendix 1).

Figure 1. Annual change in forest area by region, 1990–2010.

Source: FAO (2010).

4.2 Descriptive statistics

Table 1 reports the descriptive statistics. It shows that the average rate of long-run forest cover change per capita is negative (−0.0181) which is indicative of deforestation. Deforestation is more important in the African countries than in other developing countries. Indeed, the average rate of long-run forest cover change per capita is −0.03 in Africa versus −0.01 in the non-African sample (see tables A3 and A4 in online appendix 3). However, the positive maximum value (0.0266) means that some countries are in the process of reforestation. The average rate of long-run growth of income per capita is positive (0.020), and its smallest and highest values are, respectively, −0.0323 and 0.211. This might explain the forest cover degradation due to the scale effect of the economic activity (Grossman and Krueger, Reference Grossman and Krueger1995). The average value of the agricultural land is 0.43, which means that 43 per cent of land area is used for agriculture production. Its smallest and highest values are 0.19 and 0.85 respectively.

Table 1. Summary of descriptive statistics

Notes: ${\hat{F}_i}$ is long-run forest cover change rate per capita of country i; ${\hat{G}_i}$ is long-run growth rate of GDP per capita of country i; G_i is the log of income per capita averaged over time in country i; F_{i 0} and G_{i 0} are the log of the per capita forest area and the log of per capita GDP of the early period of country i respectively; Agri–Land_i is the agricultural land (% of land area) of country i; Deg–Open_i is the degree of openness of country i; Pop–density_i is the population density of country i; Literacy–rate_i and Pol–inst_i are the literacy rate and institutions of country i respectively.

The average value of political institutions is 7.2, well above the reference value of 2, implying that political institutions in developing countries are weaker. The mean value of literacy rate is 0.82, and its smallest and highest values are, respectively, 0.25 and 0.99. The distribution of population density variable is widely dispersed compared to the other variables. Its minimum and maximum values are respectively 1.5569 and 352.7694.

Figure 2 shows a strong negative correlation between deforestation (loss of forest cover) and economic growth, which means that deforestation tends to decrease in countries with high per capita income growth (i.e., in rich countries, such as the European & Central Asian countries), while it remains high in countries with low per capita income growth (i.e., in poor countries such as the African countries). In addition, figure 2 also shows that the relationship between deforestation (loss of forest cover) and economic growth is linear, therefore monotonic. This suggests that an EKC approach for deforestation is far from being consistent with the data.

Figure 2. Growth rate of per capita income and loss of forest cover per capita.

In contrast, notice that there is a negative relationship between countries' initial level of forest cover per capita and their subsequent change in growth rate of forest cover per capita (see figure 3). This would imply that there is a beta convergence in all countries. In other words, countries with a high rate of forest cover change (strong deforestation) will tend to converge towards those with low rates of forest cover change (low deforestation).

Figure 3. Convergence in deforestation (loss of forest cover).

Note: Forest cover per capita is in log.