Why Quantile Regression Works Well in Economics: A Partial Explanation

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 quantile 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.