pdf: An Introduction to Life-Cycle Models.
Codes for all the models can be found at: https://github.com/vfitoolkit/IntroToLifeCycleModels
(or just use this link to download as a zip)

Want to solve life-cycle models easily? Good news! Here are a series of life-cycle models that gradually build up to look at income, hours worked, consumption, and assets over the life-cycle. We will start with a deterministic life-cycle model in which people live for J periods and make decisions on how much to work. Our second model will then add a decision about how much to save (assets). Our third model will just use this model to draw a life-cycle profile. We will then step-by-step make additions to the model to understand how these help us create more realistic life-cycle profiles including idiosyncratic shocks. The intention is that you can go through the models one-by-one, first reading the pdf explanation of a given model and then running the codes and seeing how to implement it.

By the end we will have a life-cycle model in which people make consumption-savings and consumption-leisure choices, which has working age and retirement, in which earnings are hump-shaped over age (peaking around ages 45-55), the variance of both income and consumption increase with age, incomes grow in line with deterministic economic growth of the economy as a whole, people have some assets left when they die, people face the risk of substantial medical costs when old, and where borrowing constraints and precautionary savings play an important role. And we will be able to use these to plot life-cycles profiles, including the mean, variance, and Gini coefficient of a variable conditional on age, and even on 5 year age-bins. We will also be easily able to simulate panel data sets from the model on which we could run regressions. There are also some models illustrating important concepts like the role of borrowing constraints and precautionary savings.

These life-cycle models can be used easily requiring very little knowledge of numerical methods; all you need is Matlab and a gpu.

These codes take advantage of what will become version 2 of VFI Toolkit. You just refer to parameters by name, and VFI Toolkit handles the rest. You create life-cycle profiles of ‘earnings’, and then just refer to it by name. When parameters depend on age this is handled automatically. All of which leaves you to free to just get on with the economics and solving life-cycle models.

If you have any questions about the material, or spot a typo in the codes, or would just like to ask a clarifying question, etc., please use the forum: discourse.vfitoolkit.com
If you think there is anything important relating to life-cycle models that is not covered please let me know and I will think about adding another example.

Video about the Introduction to Life-Cycle models (24mins): vimeo.com/750251629 (slides)