Mathematical models of urban spatial structure in cities with decentralized employment involve the interaction between a minimum of three markets: land, labor and capital. I study the interaction between the land and the labor markets carefully. Standard theory assumes that when firms...

Conditional independence assumptions are very important in causal inference modelling as well as in dimension reduction methodologies. These are two very strikingly different statistical literatures, and we study links between the two in this article. The concept of covariate sufficiency plays...

In this note, we address the problem of surrogacy using a causal modelling framework that differs substantially from the potential outcomes model that pervades the biostatistical literature. The framework comes from econometrics, and it conceptualizes direct effects of the surrogate endpoint on...

Recently, a class of machine learning-inspired procedures, termed kernel machine methods, has been extensively developed in the statistical literature. In this note, we construct a so-called ‘adaptively minimax’ kernel machine. Such a construction highlights the limits on the...