To get a better picture of the future behavior of different economics-related quantities, we need to be able to predict not only their mean values, but also their distribution. For example, it is desirable not only to predict future average income, but also to predict the future distribution of income. One of the convenient ways to describe a probability distribution is by using alpha-quantiles such as medians (corresponding to alpha = 0.5), quartiles (corresponding to alpha = 0.25 and alpha = 0.75), etc. In principle, an alpha-quantile of the desired future quantity can depend on beta-quantiles of current distributions corresponding to all possible values beta. However, in many practical situations, we can get very good predictions based only on current quantiles corresponding to beta = alpha; this is known as quartile regression. There is no convincing explanation of why quantile regression often works. In this paper, we use an agriculture-related case study to provide a partial explanation for this empirical success -- namely, we explain it in situations when the inputs used for prediction are highly correlated.
Technical Report: UTEP-CS-22-80