inequality restrictions on parameters in estimation

[np2333]

Hi,
I just wanted to check if there is a way to impose inequality restrictions on parameters while estimating them. For instance, if i want to estimate 2 parameters a1 and a2, then how can i impose a constraint like a1<=a2, or a1+a2<=1 For the first one for instance, it is correct to dodo the following?

a1 0.5,1E-5,1, a2 BETA_PDF,0.85,0.1;

a2 0.2,1E-5,1, BETA_PDF,0.5,0.1;

[jpfeifer]

The general answer is no. However, it seems you are trying to estimate the autoregressive coefficients of an AR(2)-process. In this case you can impose that the two autoregressive roots must be smaller than 1 and then use model-local variables to recompose the autoregressive coefficients as

Code: Select all

# rho_1= (root1+root2);
# rho_2= - root1*root2;


This will assure that rho_1+rho_2<=1.

It is not correct to do:

a1 0.5,1E-5,1, a2 BETA_PDF,0.85,0.1;
a2 0.2,1E-5,1, BETA_PDF,0.5,0.1;

Dynare will not obay this upper bound and should not allow you to specify this prior. If it does, please report this and we will issue an error in future versions.

[np2333]

Hi Johannes,

thanks for your response. Actually its not an AR(2) model but something analogous to a model with decreasing returns to scale: For example:
y = a1*L+a2*K
where i want to impose the following restrictions:
1. a1>=0
2. a2>=0
3. a1+a2<=0
Anyway to do this?

Regarding the second point, dynare does obey the upper bound for a1 based on the value of a2 that i have declared in the calibration section of the model (the estimation parameter initialization block)

[np2333]

sorry the third restriction is a1+a2<=1, not 0.

[jpfeifer]

I have an idea. If you can use a steady state file for your model, you can check whether these restrictions are satisfied and just cheat Dynare by telling it the steady state did not solve when the parameter restriction is not satisfied. That way, any restriction can be imposed during estimation. The only downside you have to keep in mind is that the prior is improper in this case it won't integrate to 1 anymore and you cannot use it for model comparison.

[np2333]

thanks for the suggestion