Identification and posterior means

question 1 -
While estimating 3 parameters the Identification strength with moments Information matrix (log−scale), show no bars and matlab informs that all variables are collinear with each other.
However when I estimate any two separately the bars appear and all variables are identified.
I was wondering how to correct or explain this behaviour ?
question 2 - Also the posterior means change for parameters when I add one more parameter to the subset of parameters to be estimated ? Is there any rule of thumb if we need to estimate a certain number of parameters ? The acceptance ratio is 30%. Can increasing the number of metropolis hastings replications solve this problem ??


  1. This is a clear case of one the parameters only appearing jointly. Unless you fix one of them, there is no way of identifying them. This is the reason for the collinearity warning.
  2. This suggests that your model is misspecified with one parameter fixed at the value you consider (if you are not talking about the collinearity case, in which the parameters can be all over the place, because they are not uniquely identified). See Remark 21 (Calibration vs. Estimation) in Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models” By fixing one parameter to a wrong value, you put all the burden of accounting for the data on the other parameters. That is the reason the estimates change once you allow the fixed parameter to be different.