Hello everyone!

I’m computing two steady states simultaneously, say, relative PPI price p_{H} and home output Y_H, via the MATLAB function `fminsearch`

.

In a previous project, this function works pretty good and quick. But it reports error in my current one. Then I compare the two situations by 3D graphs and corresponding 2D contours. The x-axis is p_H, y-axis for Y_H.

The value function’s surface is fairly concave in the previous one, such that `fminsearch`

can easily find the local minimum (zero), while the surface is a bit flat/even around the true p_H and Y_H.

Since `fminsearch`

applies the homotopy algorithm, I guess the flat “shape” of the value function perplexes the simplex. Maybe a *smaller* simplex will go through (I don’t know how to set it).

To bypass this problem, I adjust `TolFun`

and `TolX`

from `1e-20`

to `1e-5`

for example. Dynare tells me two things:

First

```
Optimization terminated:
the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-20
and F(X) satisfies the convergence criteria using OPTIONS.TolFun of 1.000000e-20
```

**QUESTION 1**

It seems that as long as the `fminsearch`

session is called from the steady state block of the Dynare mod file (I write this computation in a separate MATLAB m-file, and when Dynare runs the steady state block in mod-file, Dynare calls this m-file), `TolFun`

and `TolX`

are always `1.000000e-20`

?

I notice that finally p_H and Y_H are not solved out. They do not appear in `Workspace`

window.

Second,

Dynare reports `Residuals of the static equations`

:

```
Equation number 26 : -1.9736e-05 : MarketClearing
Equation number 28 : -4.6414e-05 : CountryBudgetConstraint
```

Notice that the errors are in `1e-5`

, rather than `1e-20`

.

**QUESTION2**

Following my previous question, considering the flat shape of the value function or the nature of my model, can I change the internal precision of Dynare from `1e-20`

to `1e-5`

? After all, the default `TolFun`

and `TolX`

for `fminsearch`

itself are indeed/only `1e-4`

.

Moreover, I’m not sure whether lowering the computational precision has any significant problem for future stochastic simulation. You might suggest modifying my economic model, but it is much time-consuming!

Thank you in advance! Sincerely