New example based on model of Imrohoroglu, Imrohoroglu & Joines (1995) – A Life-Cycle Analysis of Social Security. This example solves the general equilibrium for an OLG model with standard expected utility preferences.

VFI Toolkit allows you to switch to ‘exotic’ preferences like Epstein-Zin and Quasi-Hyperbolic discounting with just a few lines of code. Here are examples that solve the exact same model again but this time using Epstein-Zin preferences and Quasi-Hyperbolic discounting preferences respectively. The only differences in the codes are in the first few lines, everything after that is identical demonstrating how easy it is to switch preferences. Two further examples show how to add endogenous labor, and how to use endogenous labor with Epstein-Zin preferences.

These examples demonstrates new features in VFI Toolkit for solving models with exotic preferences. These features are simply implemented as an option in standard value function. Note that from the perspective of simulating agent distributions there is no difference (hence you must set appropriate vfoptions, but no change to simoptions). General equilibrium commands automatically handle the exotic preferences.

Epstein-Zin preferences are useful as they seperate ‘intertemporal substitution’ from ‘risk aversion’, both of which are determined by the same parameter in, e.g., a CES utility function with (standard) von-Neumann-Morgenstern expected utility preferences. Quasi-Hyperbolic discounting captures ‘impatience’, you take actions today that are in your present interest, but are not in the longer-term interest of your future self. Both are explained in more detail in this pdf detailing the exact models that the Epstein-Zin and Quasi-Hyperbolic discounting examples are solving, as well as an explanation of their purpose. It also includes psuedo-code for the algorithms used by the VFI Toolkit. Note that there are two types of Quasi-Hyperbolic discounting, naive and sophisticated; both are implemented and can be set using vfoptions as in the example above, and naive is used by default if you do not specify.

Have also uploaded a replication of Imrohoroglu, Imrohoroglu & Joines (1995).

One paper that uses Quasi-Hyperbolic discounting is Imrohoroglu, Imrohoroglu & Joines (2003). The model is similar but different to their 1995 paper, and I link this mostly to give you a better understanding of how and where Quasi-Hyperbolic discounting might matter in terms of the Economics; beware there is a typo in their formulation of the sophisticated quasi-hyperbolic discounter’s value function problem.

I have also uploaded some examples based on the infinite-horizon Aiyagari model. Example solving the original Aiyagari model is already available. I have added a version with Epstein-Zin preferences, a version with Quasi-Hyperbolic discounting, a version with endogenous labor, and a version with both endogenous labor and Epstein-Zin preferences. All of these models are explained in the aforementioned pdf.

All of the codes implementing the Aiyagari model and the IIJ1995 model, as well as the variations using Epstein-Zin preferences, Quasi-hyperbolic discounting, Endogenous labor, and Endogenous labor with Epstein-Zin preferences, as well as the pdf explaining them can be found at: https://github.com/vfitoolkit/VFItoolkit-matlab-examples/tree/master/Exotic%20Preferences