Replication of the model in Ludwig and Schon (2018)

I read a very interesting paper by Ludwig and Schon,

Endogenous Grids in Higher Dimensions: Delaunay
Interpolation and Hybrid Methods
Comput Econ (2018) 51:463–492
Link: Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods | Computational Economics

The paper is about a generalization of the EGM to more than one dimensions. Besides this, the model used in the paper is relatively simple and I think it could be solved rather easily with the VFI toolkit, given today’s computing power on a GPU.

So I wanted to double check if indeed the VFI toolkit can handle the model in the paper :slight_smile:

I can summarize here the relevant equations.

There are two state variables, financial assets a and human capital h, and of course age j. There is no shock to earnings, only mortality risk. The choice variables are consumption c and investment in human capital i. The Bellman equation is

V(a,h,j) = max_{c,i} u(c)+prob_surv(h’)*V(a’,h’,j+1)

subject to

a’ = R(a+wh-c-i), a’>=0
h’ = (1-delta)
(h+f(i))

where f(i) is a strictly increasing, strinctly concave production function for human capital and prob_surv(h) is the per-period survival probability that is increasing in h. Note the h can be interpreted as human capital or health capital.
So the model is pretty simple, the only difficulty is that there are two continuous state variables and two choice variables, and h’ requires interpolation.

Catch is that the model is infinite horizon.

VFI Toolkit would easily solve the finite horizon version of this model (using vfoptions.experienceasset; see the Attanasio, Low & Sanchez-Marcos 2008 codes for example). But I have not implemented experienceasset for infinite horizon so currently this is not something the toolkit can solve.

They say they solve a finite horizon version with 100 periods, but I cannot see anywhere what they set for the terminal period? (V=0?)

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Actually there is a more problematic issue. Specifically, the discount factor depends on human capital. VFI Toolkit cannot presently handle this. [Eqn is in in middle of Section 2.1.2 on pg 469]

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