Marriage and Divorce in Continuous Time

TL;DR

This paper introduces a continuous-time reformulation of a marriage and divorce model using advanced stochastic methods, significantly improving computational efficiency while maintaining accuracy in key demographic outcomes.

Contribution

It replaces the AR(1) process with an Ornstein-Uhlenbeck process, enabling linear computational complexity and better performance in modeling marriage dynamics.

Findings

Model closely replicates discrete-time outcomes

Achieves substantial reductions in computation time

Maintains accuracy in marriage and divorce rate predictions

Abstract

This paper reformulates the Greenwood and Guner (2009) marriage and divorce model in continuous time using the HACT methods of Achdou et al. (2022). Replacing the AR(1) match quality process with an Ornstein-Uhlenbeck process yields a tridiagonal generator, reducing the computational complexity of both the value function and stationary distribution calculations from quadratic to linear in the number of grid points. The continuous-time model closely replicates the discrete-time equilibrium across all key outcomes, including the share of married households, the marriage rate, and the divorce rate, while achieving substantial gains in computation time and memory usage.