The formal models are inadequate in producing desirable results

If our use of natural resources precludes future generations from using these resources, then it may not be a just policy when viewed from the eyes of future generations. In particular, using Rawlsian notion of justice, when generations make decision using veil of ignorance about which generation they belong to, if they are unlikely to decide to make reservoirs, then such reservoirs are made unjustly. Sidgwick put this statement differently by demanding anonymity in such utility ranking:i.e. the outcome of a preference ordering among different welfare paths between generations shouldn’t differ based on which generation is making the decision . Unfortunately, the concept of intergenerational equity has yet to be incorporated satisfactorily in economics: the major instrument in NPV calculation is a positive discount rate that leads to the finite NPV of infinite stream of incomes. Some sort of contradictions plague almost all proposed models such as paternalistic consumption models, paternalistic utility model, Chichilinsky’s model and Alvarez-cuadrado et al is model that improves on Chichilinsky’s model by guaranteeing optimal path of renewable resource extraction.

The major problem lies in the inability of comparing these utility streams: undiscounted utility often has NPV equal to infinity and one can’t Pareto rank them , Svensson. Discounting on the other hand has always been very controversial,blueberry grow pot in particular in environmentally sensitive projects. Our model uses discounting as a tool not only to ensure the finiteness of present value of the dam, but also in incorporating the stochasticity of future developments. Other studies of reservoirs have skipped the discussion of discounting altogether. Often,sustainability frontier of a dam is defined in terms of two ratios: Kw and Kt ; where Kw is defined as above and Kt is the ratio of storage to annual sediment arrival. Basson and Palmieri et al both provide a lengthy discussion on sustainability frontier in terms of Kw; and Kt : If a non-sustainable outcome is economically desirable to a sustainable outcome, then the reservoir can’t be sustained. Such economic desirability is expressed in terms of net present value of the reservoir under the two conditions. If NPV of the reservoir under sustainable outcome is higher than the NPV under unsustainable outcome, then the reservoir is sustainable. Often, higher Kt is more likely to yield sustainable outcome than lower Kt for a given Kw:We provide a new approach to model sedimentation management problem in large reservoir. This paper contributes to existing scant literature in what is being realized as an important topic in natural resources economics. Our model allows uncertainty in sedimentation accumulation, which is useful in understanding the impact of global warming or fluctuating weather if they contribute to the change in variance of sediment arrival rate in the reservoir.

This paper also contributes by providing a new algorithm to solve a particular type of boundary value problem arising due to the quadratic nature of the cost function. Quadratic cost function leads to nonlinear second order value function. Though there are several existing algorithms to tentatively solve these equations, all of them have some deficiencies. Some , such as nonlinear shooting methods, could be very slow, while others such as finite difference method are computationally cumbersome. We provide a new nested method that is a slight modification of the projection method provided by Judd. We calibrate our model by using the data from Tarbela dam in Pakistan. Tarbela is one of the most vulnerable dams in the world right now, because of its apparently high rate of erosion. We find that the dam could be sustainably operated for a particular linear cost function, and also for the quadratic cost function. However, we note that there are other issues that could make these assertions weaker. Removing sediments, for example, would also require finding a proper place to dump those sediments. Our model is simple and yet useful in understanding the issues surrounding the reservoir management. We provided many comparative statics results such as impact of increased sediments, impact of change in discount rate and impact of increased uncertainties on both value function and control functions. In both our basic model and our definition of sustainability, we focus on the major role played by water storage level on the value of the reservoir or on the sustainability criterion. Getting useful data on large dams is still very difficult.

Dams also differ by their location, their political significance and their strategic and even psychological meaning in the host country. Each dam is also likely to have its own specific cost function of removing sediments from the reservoirs. Reservoir operators are just recently beginning to think about sustainability of the reservoirs. Tarbela’s planners had originally planned the dam to operate for fifty years, a target they don’t like to stick to anymore. While the planners are now beginning to weigh different options for sediment removal, our results show that they are not too late in implementing those strategies. Future research in sediment management should look at the risk averseness of the planner. We use a risk neutral planner in our paper. Furthermore, since privately operated reservoirs are often licensed to run for a limited period , one would want to introduce a time dependent model to study the situation of private ownership. In this situation, optimization decision will yield a partial differential equation with time as one of the arguments. The welfare impact of allowing privately held reservoirs is also important next step in this field. However, the most important of all is better understanding of cost function. Right now, the understanding of cost function in sediment removal problems is very limited and it hinders effective management of reservoirs. Also, a major weakness of the model is its assumption that V0 and VK are known. The calibration assumes that VK is the cost of construction. It is an ad hoc assumption and probably is an underestimation of the value. A better understanding of such values could be derived only by, or at least in conjuction with, other economic techniques such as non-market valuation methods. Finally, in a lot of cases, a mixed model, in which different sedimentation strategies are used together are used. Modeling such a situation is more complex,hydroponic bucket but could be one of the topics of future research.Following the concept used by Kuznet to describe income-inequality relationship , an Environmental Kuznet Curve was developed to describe relation between environmental quality and income. Generally speaking, this relationship is considered to be of a quadratic shape. This means pollution goes up to a certain point as income increases, eventually declining above a certain level of income commonly known as a turning point. This type of relationship exists because countries generally pass through an agricultural phase into an industrial phase and then finally specialize in the service sector. In the agricultural phase, countries have little pollution.

As a country transforms to an industrial phase, pollution increases-originating from both point and non-point sources. Agricultural production becomes more intensive as little emphasis is placed on improving environmental practices and more emphasis is placed on the amount of food produced. Therefore, pollution continually increases.As the country transforms its economy to the service sector, pollution declines because the country imports pollution-intensive products from abroad. Therefore, one would observe a downward trend in total pollution. Income also increases in this phase of growth. Another reason why one would observe this EKC type of behavior is due to people’s preferences. It is generally thought that environmental quality is a luxury good; therefore, as per capita income rises, emphasis is placed on increasing environmental quality. This traditional inverted U-shape of the EKC has been challenged because many researchers claim that the relationship may not be depicted in a quadratic framework. For some pollutants, one would observe a cubic pattern whereas for other pollutants for which assimilation rates are low, the pattern may be monotonically increasing. Pearson as well as Cole, Ryaner, and Bates are dissatisfied with the econometric progress on functional form specifications in the studies of the EKC. To address these concerns about the shape and econometric estimation of the income- environmental quality relationship, other functional forms of income have been proposed and the relationship between income and pollution has been modeled in a non-parametric form. Semiparametric methods have also been used; where in addition to income and its different functional forms, additional variables have been also added to the regression model . A few authors have even considered adding variables such as governance in EKC models . Yet other rauthors have been frustrated with the sensitivity of the results to the slight changes in the data used . Therefore, the EKC concepts introduced by Grossman and Krueger and popularized by the World Bank have been getting increased attention. The objective of this paper is to look at how CO2, a stock pollutant, can be related to per capita income in Latin American countries. This study explores this relationship using both parametric and semiparametric panel data models. This study also shows that a parametric quadratic relationship is rejected in favor of a semiparametric estimate. Furthermore, we used hitherto unused data on forestry acreage in our study. We reviewed literature that examines the relationship between CO2 and per capita income discussing the results found within the literature pertaining to CO2 in terms of the model used and turning points. Several papers have revealed an inverted U-Shaped EKC relationship between CO2 and income using data from various countries utilizing various econometric methods.For example, Schmalensee, Stoker and Judson studied CO2 emissions data from 141 countries for the period 1950-1991, and use a spline functional form in a two-way fixed effects model. Sengupta used a fixed effects quadratic model in addition to data from 16 developed and developing countries. Carson , Jeon, and McCubbin utilized data from U.S. states.All three of these papers found an inverted relationship between CO2 and income. Bengochea-Morancho, Higon-Tamarit and Martinez-zarzoso analyzed 16 years of data from the European Union using a polynomial quadratic along with cubic specification in parametric fixed and random effects panel models; their study discovered an inverted, Ushaped EKC when examining a selected subset of countries.Panayotou, Peterson and Sachs used feasible generalized square method to establish the presence of an inverted U-shaped EKC in a subset of the 17 developed countries in their study. Other studies supporting an inverted U-shaped EKC are Moomaw and Unruh, Friedl and Getzner , and Millimet, List and Stengos. Contrarily, there are other papers that reject the inverted, U-shaped relationship between existing between CO2 and income. For example, Shafik and Bandopadhyay claimed that one might see a monotonously-increasing relationship between CO2 and income. To reach this conclusion, their study utilized 26 years of CO2 data from 118 to153 countries as well as polynomial specification in both fixed and random effects models. Holtz-Eakin and Seden used a two way fixed effects model with a quadratic functional form to analyze data from 108 countries, and unveiled that the turning point could be as high as $8 million dollar per capita. Agras and Chapman indicated that there may not be any turning point for CO2 based on their study of 34 countries using a fixed effects autoregressive distributed lag model. Moomaw and Unruh and Dijkgraff and Vollebergh used data from OECD countries from 1950-1992 and from 1960-1997, respectively; both rejecting the presence of a quadratic relationship between CO2 and income. Nguyen, in a study using a non-parametric method, indicates that there is a convergence in CO2 release among OECD countries. This view is also supported by Strazicich and List in their analysis of 21 industrial countries for the period ranging from 1960 to 1997. Other studies have also rejected an inverted U-shaped EKC .We have observed that different authors have used CO2 data from various sources to study the EKC relationship-with data originating from the World Bank, Oak Ridge National Laboratory, World Development Indicators, World Bank, OECD environmental data sources and the International Energy Agency. The postulating of the functional form was done utilizing linear, quadratic, cubic and spline functional forms. Estimation techniques used include parametric panels, fixed and random effects models, time series method, non-parametric methods, semiparametric methods, and pooled mean group estimations.