Pollution Abatement And Stochastic Endogenous Growth

In the 1990s, economists introduced the environmental pollution problem into the endogenous growth theory. Many authors have written papers to study the environmental pollution and long-term growth problem. However, most of these papers were studied in the deterministic endogenous growth theory by using deterministic optimization method. In fact, the economic actions are full of uncertainties. In this paper, we use stochastic optimization method to discuss the pollution abatement and stochastic growth problem by introducing the pollution into the stochastic endogenous growth theory.Firstly, we consider the problem about environmental protection by the government investment. The government finances by taxes. We obtain the following results in the model that we introduce the pollution into the utility function: the optimal government investment rate in environmental protection and the optimal tax rate are obtained; the optimal income tax rate is negatively related to the externality index of pollution and the stochastic shock of output, whereas the optimal consumption tax rate is positively related to the two parameters. In the model that we introduce the pollution both into the utility function and the productive function, we assume two different productive functions and obtain that increasing the externality index of pollution is in favor of economic growth but not in favor of welfare; increasing the government investment in environmental protection is in favor of welfare, whereas the effects on growth are related to the externality index of pollution and the weight of the impact of pollution on the utility.Secondly, we consider the problem about environmental protection by the government and the individual investment. The government finances by taxes and issuing bond. In the model that we introduce the pollution into the utility function, the optimal individual investment rate in environmental protection is obtained. The government investment in environmental protection has no effect on growth. When the investment is insufficient, increasing investment has a positive effect on welfare; while when the investment is excess, increasing investment has a negative effect on welfare. The government environmental protection subsidy and the weight of the individual investment in eliminating pollution both have no effect on growth, while the effects on welfare are ambiguous. The stochastic shock of government expenditure has a positive effect on economic growth. When the stochastic shock of government expenditure is little, increasing the shock will improve welfare; while when the stochastic shock of government expenditure is large, increasing the shock will decrease welfare. The stochastic shock of output is in favor of economic growth but not in favor of welfare. In the model that we introduce the pollution both into the utility function and the productive function, we have that when the individual investment in environmental protection is insufficient, a rise of the individual investment in environmental protection is in favor of economic growth but not in favor of welfare; while when the individual investment in environmental protection is excess, a rise of the individual investment in environmental protection is neither in favor of economic growth nor in favor of welfare. Increasing the government investment in environmental protection has no effect on growth but has a positive effect on welfare. Increasing the weight of pollution abatement by the individual investment is in favor of growth but not in favor of welfare.Finally, we consider the problem about pollution abatement by the environmental protection technology. In the first model, we use the government investment and the exogenous technology to eliminate pollution. The optimal government investment rate in environmental protection and the optimal tax rate are obtained. The optimal income tax rate is negatively related to the stochastic shock of output and the stochastic shock of technology, whereas the optimal consumption tax rate is positively related to the two shocks. The expected optimal pollution is get, and in order to eliminate pollution efficiently, the economic growth should not be too fast. The second model is a two sectors model(production sector and environmental technology sector). We consider eliminating pollution by the endogenous technology for environmental protection and have the following conclusions: the optimal growth rate and the optimal allocation of physical capital and technology in two sectors and the optimal are obtained; the optimal allocation decision is independent of the the stochastic shocks and depends on the shares of the two sectors and the weight of the impact of pollution on the utility.