Bayesian estimation process has many warnings

Dear professor,
I estimate a parameter, elasticity of substitution in production function, by bayesian estimation.
codeA1.mod (8.6 KB)
obdata1120A1.xlsx (11.3 KB)

I get ‘mode check plots’, ‘Multivariate convergence diagnostic’,and ‘MCMC univariate convergence diagnostic’. The estimated mode is at the maximum of the posterior likelihood. The two lines stabilize horizontally and are close to each other.

The MODEL_DIAGNOSTICS command show “No obvious problems with this mod-file were detected”.
However, in the process of estimation, there are lots of warnings, Matrix is close to singular or badly scaled. Results may be inaccurate.
Can the result be accepted?
Thanks in advance!

The first plot suggests that the parameter is not identified. The likelihood is flat.