Discretizing earnings dynamics: implications of Gaussian-mixture shocks for life-cycle models

The standard AR(1) process with gaussian innovations, commonly used in life-cycle models of earnings dynamics, has proven insufficient. Recent research highlights the age-dependent and non-Gaussian nature of earnings changes. Empirical studies show that an AR(1) process with Gaussian-mixture innovations, along with age-dependent parameters, provides a better fit to this evidence. However, implementing such a model in a life-cycle framework requires discretization. To address this, we extend the Tanaka–Toda method and evaluate its performance. We then apply this method to a standard life-cycle model, discretizing various earnings processes to assess the impact of more realistic earnings dynamics compared to the traditional AR(1) process with gaussian innovations. We find that non-gaussian innovations and non-employment shocks are important to both annual and lifetime inequality. They also improve the performance of life-cycle models on consumption inequality and consumption insurance. Given their important impact on model results and empirical realism, the use of gaussian-mixtures provide an accessible improvement to life-cycle models. We provide Matlab code for the implementation of this discretization method.