Structural models of military retention are useful for evaluating policy alternatives that are outside historical experience. However, even relatively simple models can require significant compute time. In this report, the author shows how dynamic military retention models can be estimated using a method that avoids the need to solve dynamic programming problems — and, thus, the significant compute time required to do so.

A Model of Air Force Enlisted Retention

Theoretical Background, Implementation, and Estimates Using Conditional Choice Probability Estimation

Michael G. Mattock

ResearchPublished Sep 30, 2025

Cover: A Model of Air Force Enlisted Retention
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Structural models of military retention are useful for evaluating policy alternatives that are outside historical experience. However, estimating the parameter coefficients for these models might require solving stochastic, dynamic programs thousands of times for each individual in the data. Even relatively simple models can require significant compute time, which rises rapidly with each additional explanatory variable. Although advances both in computing power and in software over the past few decades have helped increase the size of models that are feasible to estimate, a sufficiently large number of state variables can still render dynamic programming impractical. In this report, the author documents an alternative approach to estimating the coefficients of dynamic discrete choice retention models that avoids the need to solve dynamic programming problems — and, thus, the substantial compute time required to do so.

Key Findings

The author's approach works if several key assumptions hold true

  • Stay-leave retention models without incorporating unobserved heterogeneity in the characteristics of service members can be estimated using a logit, which appreciably reduces the estimation challenges associated with using a dynamic discrete choice modeling approach to retention. These models can include independent variables that capture observed heterogeneity of characteristics and that change over time according to a Markov process.
  • Stay-leave retention models with unobserved heterogeneity can be estimated using an expectation-maximization algorithm, in which the algorithm estimates the distribution of individuals over different tastes and then estimates the rest of the model parameters, taking the estimated distributions over taste as data. These models can include independent variables that change over time according to a Markov process.
  • The population distribution of taste is constant over cohorts, the incentive structure under which enlisted members make retention decisions remains constant over time, and the population of enlisted members is in a stationary environment in which the transition probabilities and the process that generates the unobservable error do not vary over calendar time.
  • Direct application of this approach to policy simulations is restricted to historical experience in the sense that existing conditional choice probabilities that correspond to how a member would respond under a new policy would be needed to evaluate the impact of a policy.

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Mattock, Michael G., A Model of Air Force Enlisted Retention: Theoretical Background, Implementation, and Estimates Using Conditional Choice Probability Estimation. Santa Monica, CA: RAND Corporation, 2025. https://www.rand.org/pubs/research_reports/RRA3172-2.html.
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The research reported here was commissioned by the Assistant Secretary of the Air Force, Force Management Integration, and conducted within the Workforce, Development, and Health Program of RAND Project AIR FORCE.

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