Second moments of observed variables

Hi all

I am trying to run a bayesian estimate with about 7-8 variables. among them are the usual Y, C , I.

I first computed the modes. I just realized that the correlation of consumption with output is negative. I had htought that the correlation would be the same as i nthe data as
I expect to get the same consumptions series as in data with the estimated parameters.

Can anyone give a clue why I get different second moments even for the observed variables ?

Ps. There is no warnings that something is wrong and the mode graphs are ok.


Unless a miracly happens, you model will not be able to match the data perfectly. The data in a linearized model is characterized by the means and the (cross-)covariances at all leads and lags. You are doing a likelihood-based estimation. The likelihood function is a sufficient statistic for all these covariances. What the estimation does is not matching moments, but minimizing the forecast error. In that, the contemporaneous covariances are only one set of moments that is implicitly targeted. But there are also other ones, e.g. the covariances at lag 100. If you want to target only a particular set of moments, use moments matching instead of full information techniques.

Thanks Professor Pfeifer for your reply.

I was about to ask how I would do the Simul Moment Matching but then
I searched the forum and read one of your comments that refers to the replication codes for Risk Matters (2014) in AER already published.
it will take some time for me to get used to the matlab code coming with it.

Other than that it seems I have to rely on luck or intuition to get as many model-moments close to the data-moments as possible via the likelihood-max estimation.

Thanks a lot for taking your time.