I’m halfway through overhauling some parts of the Intro to Life-Cycle Models to improve explanations around using exogenous shocks.
Just wanted to add a comment that what is now Life-Cycle Model 11, which is about using i.i.d. exogenous shocks, ‘e’. This is what used to be model 11B.
What used to be 11A, which showed how to treat i.i.d. as a second markov, has now become model A11 (appendix A, model 11). It was misleading to have this as such a prominent example when it is a bad idea to take this approach. Moving to the end of appendix A hopefully makes it clearer that you should be modelling i.i.d shocks as ‘e’, and that Life-Cycle Model A11 is just about helping people more deeply understand what the markov transition matrices are.
Thanks for this update, Robert! Quick question: will this change break backward compatibility somewhere? I’m using the Markov plus iid shock (and, separatly, also the semi-exogenous shocks) in a project of mine
No changes to the actual toolkit. I’m just reworking some of the Intro to Life-Cycle Models so that it better explains how to do some more ‘advanced’ shocks [age-dependence, gaussian-mixtures, multiple markovs and multiple i.i.d., correlated shocks, etc.]
Just pushed the full overhaul of Appendix A of the Intro to Life-Cycle Models. Now covers a wide variety of shocks. Explains the three shock types: semi-exogenous, markov and i.i.d. shocks. How to use up to four of each shock type.
Also covers how to do age-dependent shocks. And how to move from ‘stacked column grids’ to ‘joint grids’ and how this can be used to handle correlated shocks.
Also explains all the discretization methods currently in VFI Toolkit. includes four main approaches to discretization: Tanaka-Toda, Tauchen, Tauchen-Hussey, & Rouwenhorst (Tanaka-Toda tends to perform the best of these). And also all the kinds of processes for which there are discretization routines: AR(1), AR(1) with gaussian-mixture innovations, AR(1) with stochastic volatility, AR(2), VAR(1), life-cycle AR(1) [life-cycle here means that it is non-stationary in the sense it changes every period], and life-cycle AR(1) with gaussian-mixture innovations. I have tried to harmonize all these discretization codes to take inputs in the same order, using same notation, and giving ordering of outputs. These discretization methods can of course be used independently of VFI Toolkit itself.
