_{1}

^{*}

The present study provides a utility maximizing theoretical framework motivating the EKC model. Theoretical parameters are linked directly to the typical empirical parameters of the reduced form empirical EKC model. Linking the theory to the typical empirically estimated parameters is relevant for devising policy and future EKC studies.

The environmental Kuznets curve (EKC) describes the relationship between income per capita and environmental degradation as an inverted U-shape. At initial stages of economic development and low income per capita, environmental degradation increases with income because increased production leads to pollution. Eventually, the environmental problems are redressed as demand for environmental quality increases with rising income.

Since the initial EKC study by [

[

Consider agent 1 in the upstream country (U) and agent 2 in the downstream country (D). The utility of agent 1 is a general function of their consumption and pollution,

and the downstream agent utility is a function of their consumption and pollution,

Utility is quasi-concave in C and P for upstream and downstream agents. Pollution in the upstream country is a function of consumption

where

Pollution in the downstream country is a function of consumption and environmental effort in the downstream country, plus the fraction of upstream pollution that travels downstream,

where

Income

where

In a specified utility function, agent

where

where

Substituting the pollution function into the utility function utility

^{1}To see this, note that the solutions to the problem are of the form

The upstream agent chooses consumption and effort to maximize utility, subject to the budget constraint^{1}. Optimal consumption and effort levels in the upstream country are^{ }

In general

Again

Pollution in the downstream country is

where

The potential of diminishing returns to pollution with respect to consumption and environmental effort is preserved from the A&L model.

Substituting (13) into (11) the utility of the downstream citizen is a function of their own consumption and environmental effort as well as upstream consumption and environmental effort,

subject to the constraint on income,

Treating

Substituting (9), (10), (15), and (16) in the downstream pollution function

and combining like terms and simplifying yields^{ }

Equation (18) requires the further restriction

The estimated EKC model follows

where

Linking the theoretical model with the empirical model, the second order marginal effects of consumption and effort on utility for the upstream country

Solving for

The parameter

The parameters

Although this model is somewhat restrictive, this appears to be the first attempt to link a theoretical model of an EKC with an empirical model. This is important because the underlying causes of an EKC are debated. Some EKC theorists believe citizens make “greener” consumption choices as they grow richer, while other theorists believe the EKC is a reflection of harsher environmental regulations in higher income countries. The EKC empirical estimates can derive underlying second order effects of consumption and effort on utility. Results may offer insight into how consumers value consumption and effort and where their income should be spent.

This paper investigates downstream dependence in an EKC for water pollution. The question this paper addresses is whether downstream pollution can be redressed with income growth in the upstream country. A theoretical model is developed that relates theoretical parameters directly with the typical empirically estimated parameters of the reduced form EKC model. Theoretical parameters for upstream and downstream county consumption and environmental effort are derived. Future EKC studies may benefit from employing the theoretical model proposed in this paper to help devise appropriate policy for various pollution indicators.

Special thanks to Jeff Peterson, John Crespi, and Henry Thompson for comments.