Environmental Engel Curves: A Neural Network Approach
用神经网络估计环境恩格尔曲线，发现家庭收入与污染呈正相关但弹性小于1，且随时间下移变凹，最后一年出现倒U形，表明中高收入家庭污染存在峰值。
Abstract Environmental Engel curves describe how households' income relates to the pollution associated with the services and goods consumed. This paper estimates these curves with neural networks using the novel dataset constructed in Levinson and O'Brien. We provide further statistical rigor to the empirical analysis by constructing prediction intervals obtained from novel neural network methods such as extra-neural nets and MC dropout. The application of these techniques for five different pollutants allow us to confirm statistically that Environmental Engel curves are upward sloping, have income elasticities smaller than one and shift down, becoming more concave, over time. Importantly, for the last year of the sample, we find an inverted U shape that suggests the existence of a maximum in pollution for medium-to-high levels of household income beyond which pollution flattens or decreases for top income earners.