Life-Cycle Model 27 is a simple exogenous labor supply model, but using the rich earnings dynamics process “Model 5” of Guvenen, Karahan, Ozkan & Song (2021). This is a state-of-the-art earnings dynamics model, and potentially the ‘best’ in the sense of hitting both cross-sectional annual earnings inequality, and the cross-section of lifetime earnings inequality. I’ve just finished adding Life-Cycle Model 27 to the Intro to Life-Cycle Models.
This process has a gaussian-mixture i.i.d shock, discretized with Farmer-Toda extension of Tanaka-Toda method (Farmer & Toda, 2017; Tanaka & Toda, 2013).
The process also has a life-cycle (non-stationary) AR(1) with gaussian-mixture innovations, discretized with KFTT extension of Tanaka-Toda method (Kirkby, 2025).
The process also has a fixed-effect which is normally distributed, and discretized by Tanaka-Toda method.
This life-cycle model is mostly about showing how you can easily build and solve models with sophisticated earnings processes.
PS. Tanaka-Toda (and it’s extensions) typically outperforms common alternative quadrature methods like Tauchen and Rouwenhorst.