DSGE Estimation - Imposing prior mean and std

I am analyzing small open economies with DSGE using Bayesian estimation technique.
As you know, we impose prior distribution about model parameters and in particular, we used to implement
pre-sample analysis when giving priors for exogenous AR (1) parameters.

So, I estimated AR(1) and got estimate of persistence parameter. (0.86)
In addition, I generated residual series and then compute standard deviation of it which is my prior mean of shock. (5.90)

However, we also have to impose prior standard deviation of persistence parameter and std of shock.

My question is that
**Is there any criteria to impose prior standard deviation of them?

Actually, I got AR(1) coefficient of 0.86 and arbitrarily imposed fairly loose prior std of 0.4 (half).

    rhoy_star, 0.80,    1E-10,   1,  BETA_PDF,0.86,0.40;

Similarly as for std of shock, I imposed

stderr epsy_star, 5.90, 1E-5, , INV_GAMMA_PDF,5.90,2.80;

But dynare shows

Error using set_prior (line 172)
Error in prior for rhoy_star: in a beta distribution with mean 0.860000, the standard error can’t be
larger than 0.346987.

Bayesian estimation is quite sensitive to the choice of prior, so that I hope to know ‘general’ or ‘good’ way on this.

Thank you.

Please see [Choosing an appropriate standard deviation for prior) and if this does not answer your question, report back. Formal prior elicitation is done in Del Negro Schorfheide (2008) - Forming priors for DGSE models.

Regarding the error message: you are using a beta distribution that implies the parameter is between 0 and 1. Given that no realizations can be bigger than 1 or smaller than 0, this limits the standard deviation that is possible. If you impose a mean of 0.86, the parameter can at most deviate from the mean by 0.14 in the right tail. You could increase the standard deviation by putting more mass in the left tail where deviations of up to 0.86 are possible, but this would at some point shift the mean. This is the intuition why your combination of mean and variance is unfeasible.