A1445
Title: Linear regression with Bouchaud's stochastic aging
Authors: Andrej Srakar - Institute for Economic Research Ljubljana (Slovenia) [presenting]
Abstract: Aging is an out-of-equilibrium physical phenomenon gaining interest in physics and mathematics. Bouchaud has proposed the following toy model to study the phenomenon. Let $ G = (\mathcal{V,E)}$ be a graph, and let $ E = \{ E_{i}\}_{i\in\mathcal{V}}$ be the collection of i.i.d. random variables indexed by vertices of this graph. The continuous-time Markov chain $ X(t)$ is considered with state space $\mathcal{V}$. The transition rates $ w_{ij}$ are defined by $ w_{ij} = \nu \exp\left(-\beta\left(\left(1-a\right)E_{i}-aE_{j}\right)\right)$. Proving an aging result consists in finding a two-point function $ F(t_{w},t_{w}+t)$ such that a nontrivial limit $ \lim_{t\rightarrow \infty(t/t_{w}) = \theta }F(t_{w},t_{w}+t = F(\theta )$ exists. The aim is to introduce ageing in a linear regression model for cross-section and panel data. Appropriate regression specifications, estimation and inference procedures are proposed. Asymptotic results are provided based on the earlier literature on probability theory and simulation studies. In an application, the effects of childhood book reading and diseases on the health status of old-age individuals using retrospective panel models are studied. Including aging in regression models is novel and opens many unexplored possibilities. As Bouchaud's trap models are also underexplored in probability theory, this promises interesting avenues for research in econometrics and probability.
