Irfs after estimation of a DSGE model

It’s about Jensen’s Inequality. Denote the IRF at parameter \theta_i with IRF(\theta_i) with N being the number of MCMC draws. Then

\frac{1}{N}\sum_{i=1}^N IRF(\theta_i)\neq IRF(\frac{1}{N}\sum_{i=1}^N \theta_i)
The first object is the mean IRF generated by estimation, while the second object is the IRF at the parameter mean generated by stoch_simul`.