Warnings

[andre]

I have a model that works well for some parameters. However, I frequently receive the following Warnings for some parameter changes:

-> Warning 1: "Warning: Matrix is close to singular or badly scaled. Results may be inaccurate." RCOND = 3.246774e-18.

It is a deterministic model with simul(periods=3000,maxit=30);

I receive the Warning above repeatedly. The RCOND continues to fall until 2.295887e-41. After this point, the warning changes to

-> Warning 2: "Warning: Matrix is singular to working precision."

I can usually circumvent these warnings with different guesses for the steady state and changing the way in which the model equations are written. However, there is a parameter that I need to increase, but that I could not find a solution. I also want to write the equations of the model in a more robust way.

My questions are:

1. In which moment of the Dynare processing I receive the warnings above. Is it because Dynare cannot find the transition path, at the simul() command?

2. If I use "exp(x)" instead of "x" for the endogenous variables, will it smooth the equations in a way that I do not receive these Warnings?

3. If I linearize the more complex equations of the model, will it solve the problem?

Thank you!

[jpfeifer]

1. Think about the exercise as finding the root of a nonlinear equation. In a Newton type solver you need to invert matrices. If the matrix is close to singular, the warning will pop up.
2. That can be, but is not a general property. In some cases using a log transformation will make the problem more well-behaved in others it makes it worse.
3. Yes, it will. Solving a linear system of equations is straightforward. But when doing so you incur an approximation error. This the cost of replacing a nonlinear problem with a linear one.

[andre]

That's great, thank you for your reply. I will implement the steps above, then. It seems that this is the right direction. Is RCOND the determinant of the matrix to be inverted?

1. Think about the exercise as finding the root of a nonlinear equation. In a Newton type solver you need to invert matrices. If the matrix is close to singular, the warning will pop up.
2. That can be, but is not a general property. In some cases using a log transformation will make the problem more well-behaved in others it makes it worse.
3. Yes, it will. Solving a linear system of equations is straightforward. But when doing so you incur an approximation error. This the cost of replacing a nonlinear problem with a linear one.

[jpfeifer]

It's the reciprocal condition number of the matrix to be inverted. See http://de.mathworks.com/help/matlab/ref/rcond.html?refresh=true

[andre]

Thank you. It is a good explanation about the rcond function and the reciprocal conditional number in MatLab. Thanks