Testing the Environmental Kuznets Curve Hypothesis: An Empirical Study for Peru

This research analyzes the Peruvian engagement against climate change through the impact of the per capita income on the environmental pollution in the national scenario during the annual period of 1980-2019. For this, the logic of the Environmental Kuznets Curve will be used, in which an “inverted U” curve shape affirms that the economic growth is favorable for the environment in the long term because an optimal income point is reached and pollution begins to decline. For this analysis, the national exports are included as a third variable, and also is considered a cubic regression equation to the original Kuznets model. Through the estimation by Dickey-Fuller and Phillips-Perron unit root tests, Granger Causality Test, the Vector Autoregression Model (VAR) method and the Forecast Graphics, it is shown that, similar to other countries of the region, Peru is actually on the initial part of the curve, where income and pollution have a growing direct relation. Finally, the models that fitted the relationship of these variables were the original model and the model with exports included.


INTRODUCTION
Peru's economic growth over the last 40 years has generated greater extraction of national natural resources, affecting more environmental quality. In the years 1990-1999, Peru grew at an average annual rate of 3.9%. The following decade, 2000-2009, the average annual growth rate was 5.6%, and finally, in the years 2010-2019 it was 4% (Ministry of Economics and Finance, 2020). This entire economically favorable scenario for Peru is due to an increase in extractive activities (agriculture, livestock, fishing, manufacturing and extraction of oil, gas, minerals, among others), affecting the preservation of our biodiversity and contributing to environmental deterioration.
Actually, a large number of investigations purpose to evaluate the impact of economic growth within the environment. For this, several researchers decided to use an accessible methodology that would demonstrate the relationship between these variables, both in the short and long term, through the Environmental Kuznets Curve (Grossman and Krueger, 1995). This theory proposes an inverted U relationship between economic growth and environmental deterioration, since as economic growth increases, environmental deterioration has the same behavior; however, there is a turning point where this direct relationship becomes inverse, and environmental degradation begins to diminish while economic growth continues its course. This criterion was applied in both developed and emerging countries, evidencing the existence of the relationship between economic growth and the environment. However, developed countries had already reached the turning point and showed a decrease in pollutants while there was economic growth; this was not the case in most developing countries, as many of them are still in the first part of the curve (Vergara et al., 2018). This Journal is licensed under a Creative Commons Attribution 4.0 International License The following research is important because its purpose is to study the type of relationship between economic growth and environmental pollution based on the Kuznets Environmental Curve for Peru, during the period 1980-2019, given the increase in carbon dioxide emissions and concern for environmental wellbeing at the national level (Ministerio del Ambiente del Perú, 2011). In addition, determine the stage of the EKC in the Peruvian economy and compare it with other countries in the region. On the other hand, it is necessary to reinforce the formulation and monitoring of the country's environmental policies for the benefit of sustainable development, all in order to ratify Peru's commitment to environmental issues at the national and international level.
It is worth mentioning that for this research the level of exports will be included in the study, in order to determine their contribution to economic growth and, therefore, their direct or indirect relationship with environmental pollution. Finally, recognize that the quadratic model better expresses the EKC compared to the cubic model for the Peruvian economy.

THEORY AND LITERATURE REVIEW
The Environmental Kuznets Curve (EKC) is an application of the Kuznets Curve to the environmental field (Kuznets, 1955), in order to explain the relationship between economic growth and the level of pollution of an economy by means of an "inverted U." The theory states that economic growth is favorable for the environment in the long term, since in a first phase, the income level increases and pollution has the same tendency, but an optimal entry point is reached where pollution begins to go down, since individuals have sufficient income to cover their basic needs and decide to take initiatives to better care for the environment. Grossman and Krueger (1991) were the first to apply the EKC mechanism, seeking to explain the empirical relationship between environmental quality and per capita GDP levels through the following model: Where "E" is the level of emissions per capita at time "t," and "Y", "Y 2 " e "Y 3 " refers to per capita income, income squared and cubed respectively at time "t." Likewise, there are the "β's" which will give the following results: If β 1 > 0, β 2 < 0; β 3 = 0, gets the original EKC.
If β1 1 < 0, β 2 > 0 y β 3 < 0, means that environmental degradation will show an inverted "U", showing that in the long term emissions will decrease but will also increase at certain turning points.
Likewise, Panayotou uses the same mechanics, and based on his research, he shows us a more concise idea of the EKC and its relationship with the main economic industries. According to the author, the highest levels of pollution occur at lower levels of income given the change from an agricultural economy to an industrialized one; and at higher income levels, the change from an industrialized economy to one based on services allows a decrease in the polluted intensity (Panayotou, 2003) (Figure 1).
The pioneers in conducting this study were Grossman and Krueger, where the term Environmental Kuznets Curve (EKC) is introduced to the "inverted U" relationship of the level of income and pollutant emissions (Grossman and Krueger, 1995). Using a data panel for the information collected from the Global Environment System (GEMS), the level of air pollution in urban centers was determined through sulfur dioxide (SO2) and total suspended particles in 42 and 29 countries respectively. Likewise, for hydrographic basins, 287 rivers from 58 different countries were analyzed during the years [1979][1980][1981][1982][1983][1984][1985][1986][1987][1988][1989][1990]. Using the mentioned variables through equations in a reduced form in the data panel, it was concluded that the inflection point for the "inverted U" varies according to the type of pollutant; also, the results agreed that the "Turning Point" was generated with an income level less than US$ 8000.
More recently, Sarkodie and Strezov (2019b) employs bibliometric and meta-analysis techniques to analyze historical trends on the EKC hypothesis. The meta-analysis reveals that studies validating the inversed-U shaped relationship observe an average of US$ 8910 as the turning point of annual income level. Most of the studies are based on atmospheric indicators, whereas, oceans, seas, coasts, biodiversity and freshwater indicators are sporadic and limited on EKC hypothesis.
Few studies test the EKC hypothesis on developing countries (Sulemana et al., 2017). Economic growth in developing countries will be more carbon-intensive comparing to developed countries as technological advancement and innovation effects. Early stages of economic development are characterized by a high use of resources which inexorably contribute to increasing ecological footprint and reducing the biocapacity (Sarkodie and Strezov, 2018). Developing countries in Latin America or Africa are also the most vulnerable to climate change and its effects (Sarkodie, 2018).

Materials
This research considers data under study in annual, stationary and longitudinal time series. All of them were extracted from secondary sources, such as the World Bank and the Central Reserve Bank of Peru. The data under study consists of an annual sample of 40 observations, ranging from 1980 to 2019. All variables were transformed into natural logarithms, obtaining the following: Carbon dioxide (LCO2t) expressed in metric tons per capita, GDP per capita (LGDPt) expressed in thousands of US$ and national exports (LEXPORTSt) expressed in thousands of US$. All tests were carried out through the Eviews program, version 10.

Empirical Analysis
In the first place, the descriptive statistics of the variables under study were calculated, it should be noted in this section that, due to the high levels of volatility of the variance, the variables were transformed into natural logarithms, in order to obtain a smoothing in the data under study as applied by Vergara et al. (2018) and Mullo Parco (2018)  Consider that for the present tests a significance level of 5% was used.
Then, we proceeded to estimate 3 optimal models for the investigation that derive from the original Kuznets equation, these are the following: Original model (a): Original model and exports (b): Kuznets model in cubic regression (c): Where: LCO2 t : carbon dioxide emission for Peru in natural logarithm LGDP t : GDP per capita in natural logarithm LGDP t 2 : Natural logarithm of GDP per capita squared LGDP t 3 : Natural logarithm of GDP per capita cubed LEXPORTS t : National exports in natural logarithm. β 0 : Kuznets environmental curve econometric model constant β 1 : GDP per capita parameter β 2 : Per capita GDP parameter squared β 3 : Per capita GDP parameter cubed ε t : Error emission variable.
Once the proposed models were defined, we proceeded to estimate which of them will be the optimal model for the investigation through the methodology of vector autoregressive models (VAR). Finally, for the environmental Kuznets curve to be fulfilled, there must be a maximum point whose parameters must be 1 positive and 2 negative.

RESULTS
At first, the Dickey-Fuller Test and Phillips-Perron Test are used to verify the presence of unit root in the variables. From that, the results are displayed in Table 1: For both Dickey-Fuller and Phillips-Perron Tests, it is obtain that the three variables in study (LCO2t, LGDPt, LEXPORTSt), on its level, has a p-value greater than 5% significance level.
Both for the Dickey-Fuller and Phillips-Perron test, in the three variables under study (lnCO2t, lnGDPt and lnEXPORTS) it was obtained that, at their level, they have a P-value greater than the significance level of 0.05 in the tests with intercept, intercept and trend and without any of the above, obtaining non-stationary series. Therefore, we proceeded to look for stationary series, for this we worked with the first differences, for all cases the P-value is lower than the significance level of 0.05, so that the null hypothesis that there is a root is rejected unitary and it is concluded that the series is stationary in first difference; therefore, the variables DlnCO2t, DlnGDPt and DlnEXPORTS are obtained. However, based on the literature previously presented, it was decided to work with the transformed variables with natural logarithms.
Afterwards, the 3 optimal models were estimated through vector autoregressive models (VAR) with the sole purpose of estimating which regression best suits our research and which one would better explain the EKC for the Peruvian economy. As a first step, it was determined to find the selection criterion of the optimal lag, choosing the smallest, it was decided to work with the Akaike Information Criterion (AIC).

Original Model Based on the Environmental Kuznets Curve (EKC) with Logarithm
Once the optimal lag, which is 2, was obtained, the VAR corresponding to the model was estimated. With respect to the R-squared values, the three equations show a high level of goodness of fit ( Table 2).
In addition, the Granger causality test was performed in a VAR model where it was obtained that the first block where the regressor is the LCO2 series and the P = 0.0402 is less than the significance level 0.05, for this it is concluded that the null hypothesis that the series should be omitted and these do cause in the Granger sense when returning (Table 3). Likewise, for the second and third block we have the variables LGDP and LGDP 2 , where the P = 0.2001 and 0.1832 respectively, being greater than the significance level 0.05; therefore, the null hypothesis that the series should be omitted and do not cause the regressors in the Granger sense is not rejected.

Original Model Based on the EKC Including Variable Exports and Logarithm
Once the optimal lag, which is 1, was obtained, the VAR corresponding to the model was estimated. With respect to the R-squared values, the four equations show a high level of goodness of fit (Table 4).
On the other hand, in the Granger causality test for a VAR model, it is obtained that the p-value of the variable LCO2 is less than the significance level of 5% with 0.0055, this means that the null hypothesis is rejected that the series should be omitted and they do cause in the Granger sense to return. On the other hand, the variables LGDP, LGDP 2 and LEXPORTS have P-values greater than 5% of significance level with 0.1701, 0.1355 and 0.075 respectively (Table 5). Therefore, the null hypothesis that the series should be omitted is not rejected and they do not cause in the Granger sense to return.

Original Model Based on the EKC in Third Degree Polynomial Regression
Once the optimal lag, which is 5, was obtained, the VAR corresponding to the model was estimated. Based on the R-squared values, the four equations show a high level of goodness of fit (Table 6).
Following this, the Granger causality test was carried out in a VAR model, for the LCO2 series, the p-value is less than the significance level of 0.05 with 0.0000, which is why the null hypothesis is rejected that the series should be omitted, concluding that the omitted series causes in the Granger sense to return (Table 7). On the other hand, the p-values of the series LGDP, LGDP 2 and  LGDP 3 are greater than the significance level of 0.05 with 0.3721, 0.3398 and 0.3072 respectively, which is why the null hypothesis that the series should be omitted, concluding that these do not cause Granger to each of their returning.
On the other hand, the impulse response analysis was performed for the VAR for the three models. In model (a), according to the LCO2 series, a slight response (value changes) can be noticed and it is mainly explained by own impulses throughout the 10 periods. With respect to model (b), according to the LCO2 and LEXPORTS series, slight moderate responses can be observed that are explained by own impulses throughout the 10 periods. Finally, the impulse-response of the model (c) the LCO2 series remains intact for the four graphs and there are no movements and sudden or slight changes of the same returning. For the three cases, with respect to the series LGDP and LGDP 2 , their responses are explained by impulses from the other returning.     For both models (a) and (b), the curve continues to rise and has not yet reached its optimum point called Turning Point where it begins to descend, this means that the Peruvian economy is located before the point of inflection ( Figure 2).
Finally, after having carried out all the corresponding tests, the following is concluded from model (c): This third model presents multi-collinearity problems, according to the literature, one way to correct this problem is by suppressing those variables that are correlated with each other, helping to reduce collinearity (Wooldridge, 2015). Therefore, it is decided to suppress the variable GDP 3 as it is not really significant to the model, since the model originally proposed by Kuznets was the quadratic equation but not the cubic one. Therefore, model (c) is discarded within our research, having as valid models only models (a) and (b).

DISCUSSION AND CONCLUSION
The following research analyzed the relationship between economic growth and environmental pollution based on the Kuznets Environmental Curve for Peru during the period from 1980 to 2019, given the increase in carbon dioxide emissions and concern for environmental well-being at national level. According to the results, the economic growth expressed in GDP per capita does influence the levels of environmental pollution during the years 1980 to 2019. However, the "inverted U" of the Kuznets Environmental Curve would not be shown since Peru as a developing country still presents high levels of inequality in income distribution, which delays reaching the "Turning Point" that would lead to a decrease in pollution levels as the level of per capita income increases.
As observed in similar developing countries, the shape of an "inverted U" is not yet presented (Reyno, 2005). However, there is a direct relationship between the emission of pollutants expressed in CO2 and per capita income, indicating that Peru is still in the first part of the curve. In Colombia, Correa (2005) conclude that for carbon dioxide, sulfur dioxide and biological oxygen demand, the Environmental Curve of Kuznets is in the growing phase. Similarly, Vergara et al. (2018) applied the logic of the Kuznets Environmental Curve to 9 South American countries during the years 2000-2012. In this research, the assumption of the "inverted U" relationship between carbon dioxide and per capita income is not met; concluding that, within the years of study, the relationship between CO2 and GDP per capita is monotonously increasing, coinciding with the results obtained in our research. Within the national antecedents, Huanchi and Calsin (2018) sought to determine the relationship between economic growth and environmental deterioration, expressed in carbon dioxide and sulfur dioxide, for the Peruvian economy during the years 1910-2010. As a result, they obtained that within the period under study there is a stable long-term relationship between economic growth and environmental degradation, concluding that Peru is still in the growth stage in reference to the EKC. This supports once again the results obtained in this research, since, despite having carried out a more updated study (data until 2019), the direct positive relationship between both variables is still seen, supporting that the Peruvian economy does not reach the long-awaited "Turning Point".
Likewise, after doing the econometric tests on the quadratic and cubic model, it is concluded that the quadratic model better expresses the EKC for the Peruvian economy since its variables are significant, unlike the cubic model that had multicollinearity problems due to the presence of the variable GDP 3 . These results confirm that, although an attempt was made to implement a study with a cubic variable to know the long-term behavior of the model, for our variables it works correctly in the quadratic model within the period under study .
Given the current situation of Peru in terms of development, if it is desired to reach the optimal income level to improve environmental quality levels in the medium term, the Peruvian State must not only focus its efforts on regulations in favor of the environment, it must also prioritize reducing the levels of inequality within the country. With a better distribution of wealth, there would be greater equality of opportunities for the population. One way to contribute to the reduction of inequality within Peru is by providing better education in the most remote areas of the country, with the purpose that they are better trained and, in the future, can access quality and better paid jobs. In the same way, the creation of financial inclusion programs will allow more people to have access to credits, savings, transactions, among others. The measures previously described would contribute to the growth of the gross domestic product from a higher level of consumption, investment, tax collection, among others, which in the long term would also be reflected in an environmental improvement.
Finally, policies are recommended to promote other productive sectors and not only focus on primary and extractive activities as the main source of income. Through training, tools and innovation, the same residents could dedicate themselves to the transformation of goods and the services sector, seeking in the medium term to specialize in it and not only dedicate themselves to extraction, which would provide greater added value to their products, obtaining higher levels of incomer per capita from exported products/services and; therefore, seeking to improve environmental quality in the short, medium and long term.