# Chatgpt and the Toolkit
**URL:** https://discourse.vfitoolkit.com/t/chatgpt-and-the-toolkit/650
**Category:** Uncategorized
**Created:** [May 15, 2026, 8:31pm UTC](https://discourse.vfitoolkit.com/t/chatgpt-and-the-toolkit/650 "2026-05-15T20:31:33Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@aledinola](https://discourse.vfitoolkit.com/u/aledinola)
#### Post date: [May 15, 2026, 8:31pm UTC](https://discourse.vfitoolkit.com/t/chatgpt-and-the-toolkit/650/1 "2026-05-15T20:31:33Z")
I typed a relatively lazy prompt in chatgpt asking how to solve the stochastic neoclassical growth model with the vfi toolkit developed by R Kirkby. I was curious to see how well AI is aware of the toolkit. This is the answer and is pretty good, given that I got it at the first try: no follow-up interactions, no context like “where to find the toolkit repo”, how it works etc.
My prompt:
_Can you explain how to solve a value function iteration problem (e.g. neoclassical growth model with tfp shocks) using the vfi toolkit by Robert Kirkby?_
**Chatgpt answer:**
# Solving a VFI Problem with VFI Toolkit
The key idea is: **with VFI Toolkit you do not write the Bellman loop yourself**. You give the toolkit:
1. grids for endogenous and exogenous states;
2. the Markov transition matrix for shocks;
3. a **return function** ;
4. parameter names;
5. options;
and then call `ValueFnIter_Case1`.
The toolkit is designed for fully discretized dynamic programming problems and can automatically use CPU/GPU parallelization.
* * *
## 1. Example model
Take the stochastic neoclassical growth model:
$
V(k,z)=\max\_{k’\in \mathcal K}
\left{
u(c)+\beta \sum\_{z’} \pi(z’|z)V(k’,z’)
\right},
$
subject to
$
c = \exp(z) k^\alpha + (1-\delta)k - k’,
$
with
$
z’ \sim \Pi(z’|z).
$
Here:
- endogenous state: k;
- exogenous state: z;
- endogenous next-period state / choice: k';
- no additional static choice d.
In VFI Toolkit terminology, this is a **Case 1** problem: one endogenous state that evolves according to the chosen next-period value, plus an exogenous Markov state.
* * *
## 2. Write the return function
The return function should take current state values and choice values as scalar inputs. For this model, the return function is something like:
```matlab
function F = StochasticGrowth_ReturnFn(kprime_val, k_val, z_val, gamma, alpha, delta)
F = -Inf;
c = exp(z_val)*k_val^alpha + (1-delta)*k_val - kprime_val;
if c > 0
if gamma == 1
F = log(c);
else
F = c^(1-gamma)/(1-gamma);
end
end
end %end function
```
The important convention is:
```matlab
ReturnFn(kprime, k, z, parameters...)
```
because k' is the choice and k,z are current states.
* * *
## 3. Define parameters
You typically put parameters in a structure:
```matlab
Params.beta = 0.96;
Params.gamma = 2.0;
Params.alpha = 0.36;
Params.delta = 0.08;
```
Then you tell the toolkit which parameter enters the discount factor:
```matlab
DiscountFactorParamNames = {'beta'};
```
and which parameters enter the return function:
```matlab
ReturnFnParamNames = {'gamma','alpha','delta'};
```
This is one of the toolkit’s main design choices: instead of hard-coding parameters into the return function, you tell the toolkit which fields of `Params` to pass to the return function.
* * *
## 4. Create grids
For capital:
```matlab
n_k = 500;
k_min = 0.1;
k_max = 50;
k_grid = linspace(k_min, k_max, n_k)';
```
For TFP shocks, suppose you already discretized an AR(1)
$
z’ = \rho z + \varepsilon’,
\qquad
\varepsilon’ \sim N(0,\sigma^2).
$
You need:
```matlab
z_grid % n_z by 1 vector
pi_z % n_z by n_z transition matrix
```
For example:
```matlab
n_z = 7;
rho = 0.9;
sigma = 0.02;
[z_grid, pi_z] = TauchenMethod(n_z, 0, rho, sigma, 3);
```
The exact Tauchen/Rouwenhorst function depends on what you use. The important point is that both k and z must be discretized.
* * *
## 5. Tell the toolkit the dimensions
For this problem:
```matlab
n_d = 0; % no additional discrete/static decision d
n_a = n_k; % endogenous state grid size
n_z = length(z_grid);
```
The toolkit uses the notation `a` for the endogenous state, so in a growth model you can think of
$
a \equiv k.
$
Then:
```matlab
d_grid = [];
a_grid = k_grid;
```
* * *
## 6. Call `ValueFnIter_Case1`
The core call is:
```matlab
ReturnFn = @StochasticGrowth_ReturnFn;
vfoptions = struct();
[V, Policy] = ValueFnIter_Case1( ...
n_d, n_a, n_z, ...
d_grid, a_grid, z_grid, pi_z, ...
ReturnFn, Params, ...
DiscountFactorParamNames, ReturnFnParamNames, ...
vfoptions);
```
Conceptually, this computes:
V(k\_i,z\_j) = \max\_{k'\_m} \left[u\left(\exp(z\_j)k\_i^\alpha + (1-\delta)k\_i-k'\_m\right) + \beta \sum\_{\ell} \pi\_{j\ell}V(k'\_m,z\_\ell) \right].
So `V` is the value function on the grid, and `Policy` gives the optimal index/value of k', depending on the toolkit version and options. In most VFI Toolkit examples, the policy is stored in an index form that you can convert back to levels using the relevant grid.
* * *
## 7. Interpret the policy
Suppose `Policy` contains indices of optimal k'. Then you can recover the policy in levels as:
```matlab
KprimePolicy = k_grid(Policy);
```
Then you can plot, for example, the policy at the median TFP shock:
```matlab
z_mid = ceil(n_z/2);
figure;
plot(k_grid, KprimePolicy(:,z_mid), 'LineWidth', 2);
xlabel('k');
ylabel('k'' policy');
title('Capital policy function');
```
You can also compute consumption:
```matlab
CPolicy = zeros(n_k,n_z);
for iz = 1:n_z
CPolicy(:,iz) = exp(z_grid(iz))*k_grid.^Params.alpha ...
+ (1-Params.delta)*k_grid ...
- KprimePolicy(:,iz);
end
```
* * *
## 8. Full skeleton
Putting the main pieces together:
```matlab
clear; clc;
%% Add VFI Toolkit to path
% addpath(genpath('C:\path\to\VFIToolkit-matlab'));
%% Parameters
Params.beta = 0.96;
Params.gamma = 2.0;
Params.alpha = 0.36;
Params.delta = 0.08;
DiscountFactorParamNames = {'beta'};
ReturnFnParamNames = {'gamma','alpha','delta'};
%% Capital grid
n_k = 500;
k_min = 0.1;
k_max = 50;
k_grid = linspace(k_min, k_max, n_k)';
%% TFP grid
n_z = 7;
rho = 0.9;
sigma = 0.02;
% You need to provide this using your preferred Tauchen/Rouwenhorst function.
% z_grid: n_z by 1
% pi_z: n_z by n_z
[z_grid, pi_z] = TauchenMethod(n_z, 0, rho, sigma, 3);
%% VFI Toolkit dimensions
n_d = 0;
n_a = n_k;
d_grid = [];
a_grid = k_grid;
%% Return function
ReturnFn = @StochasticGrowth_ReturnFn;
%% Options
vfoptions = struct();
%% Solve
[V, Policy] = ValueFnIter_Case1( ...
n_d, n_a, n_z, ...
d_grid, a_grid, z_grid, pi_z, ...
ReturnFn, Params, ...
DiscountFactorParamNames, ReturnFnParamNames, ...
vfoptions);
%% Recover policy in levels, if Policy stores indices
KprimePolicy = k_grid(Policy);
%% Plot
z_mid = ceil(n_z/2);
figure;
plot(k_grid, KprimePolicy(:,z_mid), 'LineWidth', 2);
xlabel('k');
ylabel('k''');
title('Capital policy function, median TFP state');
```
and the return function file:
```matlab
function F = StochasticGrowth_ReturnFn(kprime_val, k_val, z_val, gamma, alpha, delta)
F = -Inf;
c = exp(z_val)*k_val^alpha + (1-delta)*k_val - kprime_val;
if c > 0
if gamma == 1
F = log(c);
else
F = c^(1-gamma)/(1-gamma);
end
end
end %end function
```
* * *
## 9. What the toolkit is doing internally
Internally, the toolkit is essentially doing what you would do by hand:
1. For each current state (k,z),
2. loop over feasible k' on the grid,
3. compute current utility,
4. compute expected continuation value,
EV(k',z) = \sum\_{z'} \pi(z'|z)V(k',z'),
1. maximize over k',
2. iterate until convergence.
The advantage is that you do not manually write the large loops, the expectation step, or the CPU/GPU parallelization.
* * *
## 10. Relation to hand-written VFI
Hand-written VFI:
```matlab
for ik = 1:n_k
for iz = 1:n_z
for ikp = 1:n_k
...
end
end
end
```
VFI Toolkit version:
```matlab
[V, Policy] = ValueFnIter_Case1(...);
```
But you still need to supply the economic structure correctly:
| Object | Meaning in growth model |
| --- | --- |
| `a_grid` | capital grid k |
| `z_grid` | TFP grid z |
| `pi_z` | Markov transition matrix for z |
| `ReturnFn` | one-period utility u(c) |
| `Params` | parameters |
| `DiscountFactorParamNames` | usually `{'beta'}` |
| `ReturnFnParamNames` | e.g. `{'gamma','alpha','delta'}` |
| `Policy` | optimal k' choice, usually as grid index |
The main mental shift is that **k' is not listed as a separate decision grid `d_grid`**. In Case 1, the next-period endogenous state a' is automatically treated as a choice over `a_grid`. You only use `d_grid` for additional choices, such as labor n, portfolio shares, default decisions, etc.
---
### Author:  [@aledinola](https://discourse.vfitoolkit.com/u/aledinola)
#### Post date: [May 15, 2026, 8:43pm UTC](https://discourse.vfitoolkit.com/t/chatgpt-and-the-toolkit/650/2 "2026-05-15T20:43:04Z")
One slight imprecision: Chatgpt 5.5 suggests to define explicitly the input `ReturnFnParamNames`. This is formally correct but no longer required since **v2** of the Toolkit. The toolkit nowadays is able to figure out automatically what are the inputs to `ReturnFn` after the control/state variables.
Maybe this new feature is not well documented and/or that are not many toolkit examples using this feature? Seems strange since most examples on the official repo do not pass anymore `ReturnFnParamNames`. Perhaps old replications…
---
### Author:  [@robertdkirkby](https://discourse.vfitoolkit.com/u/robertdkirkby)
#### Post date: [May 16, 2026, 12:23am UTC](https://discourse.vfitoolkit.com/t/chatgpt-and-the-toolkit/650/3 "2026-05-16T00:23:35Z")
Impressive. Only caveat is that this is a model that has been solved with the toolkit. I have been thinking to ask something like “here is paper about a life-cycle model from the 2000s, write code in VFI Toolkit code to solve the model and produce the Table 1 and Figure 1”.
Yeah, explicitly spelling out the `ReturnFnParamNames` is something you haven’t had to do for years, but I guess there might still be the odd old code that still uses it, maybe in the AI training data set? That might make sense, for sure Open AI use the entirety of github in training (they have plenty of deals with Microsoft).
---
### Author:  [@robertdkirkby](https://discourse.vfitoolkit.com/u/robertdkirkby)
#### Post date: [May 16, 2026, 12:24am UTC](https://discourse.vfitoolkit.com/t/chatgpt-and-the-toolkit/650/4 "2026-05-16T00:24:26Z")
Also, I am trying as part of cleaning up VFI Toolkit to have more stuff to spell out to AI what it should be doing when writing code.