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Marriage and Divorce in Continuous Time

Kazuharu Yanagimoto

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.

Marriage and Divorce in Continuous Time

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.
Paper Structure (13 sections, 30 equations, 3 figures, 3 tables, 2 algorithms)

This paper contains 13 sections, 30 equations, 3 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Model
  3. Discrete-time Model
  4. Continuous-time Model
  5. Estimation
  6. Calibration
  7. Results
  8. Conclusion
  9. Computational Details
  10. Discrete-time Model
  11. Continuous-time Model
  12. Computational Complexity
  13. Supplemental Figures and Tables

Figures (3)

  • Figure 1: Replication of Fig. 6 in Greenwood and Guner ( ref-greenwood2009). The left panel shows the share of married population under the CT and DT methods. The right panel plots the utility difference $v(p,w,2) - v(p,w,1)$.
  • Figure 2: Replication of Fig. 7 in Greenwood and Guner ( ref-greenwood2009). CT hazard rates are converted to annual probabilities via $1 - e^{-r}$ for comparability with DT.
  • Figure 3: Computational Performance of Continuous-Time and Discrete-Time Methods. Benchmarked with BenchmarkTools.jl ( ref-chen2016) on an Apple M3 Max (16-core, 128 GB RAM).