High correlation in observation data

Dear all,
I have two series in my observation data, namely CPI inflation and PPI inflation, which are highly correlated (with correlation coefficient of 0.91) and this does not allow me to use both of them in my Bayesian estimation. I have one idea to regress one on the other and use the residual as a proxy of it. Is it correct? Does anyone have any idea?

I don’t see why you cannot use both in estimation. See e.g. Canova’s slides at http://apps.eui.eu/Personal/Canova/Teachingmaterial/bayes_dsge_topics_imf2014.pdf, Section 3 Practical issues

Thanks for your reply. When I use both cpi and ppi inflation together in estimation I get the following error which is a sign of singularity:
initial_estimation_checks:: The forecast error variance in the multivariate Kalman filter became singular.
initial_estimation_checks:: This is often a sign of stochastic singularity, but can also sometimes happen by chance
initial_estimation_checks:: for a particular combination of parameters and data realizations.
initial_estimation_checks:: If you think the latter is the case, you should try with different initial values for the estimated parameters.

ESTIMATION_CHECKS: There was an error in computing the likelihood for initial parameter values.
ESTIMATION_CHECKS: If this is not a problem with the setting of options (check the error message below),
ESTIMATION_CHECKS: you should try using the calibrated version of the model as starting values. To do
ESTIMATION_CHECKS: this, add an empty estimated_params_init-block with use_calibration option immediately before the estimation
ESTIMATION_CHECKS: command (and after the estimated_params-block so that it does not get overwritten):

Error using initial_estimation_checks (line 143)
initial_estimation_checks:: The forecast error
variance in the multivariate Kalman filter became
Although it says this may happen by chance, but when I use just one of the inflations in estimation, the estimation follows without any error!

I see. But that is a problem that PPI and CPI are linearly dependent and do not have a separate role in your model.

And according to your point, I’m forced to calibrate some of standard error of shocks because I have implicit inflation targeting which follows an AR(1) process and I was using PPI inflation for mark-up shock and CPI inflation for inflation targeting shock.

Sorry, but I am not following. Please explain your thoughts in more detail.

We know that we can use as many observable variables for estimation as number of shocks and the data we are using should be chosen based of model shocks. Now I have 14 shocks in my model and between them a shock is mark-up shock and the other implicit inflation targeting shock. The observable variable which I use for the first shock is PPI (or GDP deflator) and for the second shock is CPI inflation. According to your point, in my model CPI inflation is a linear function of PPI inflation and this makes me to use just one of them in estimation, so I have less observable variables than shocks. Therefore, I should calibrate the stderr of inflation targeting shock because it’s not identified.

I think you are confusing a couple of things here. You need to have at least as many shocks as non-linearly dependent observables. The Dynare error on stochastic singularity indicates that CPI and PPI are linearly dependent. But there is not unique mapping from shocks to observables as you seem to believe. It is no problem to have fewer observables. Often all parameters are well-identified. You can test this with the identification-command.

I completely understand what you’re saying and I tested identification before which revealed that all parameters are identified even inflation targeting shock. But may be I didn’t explained it well. What I mean is that I’m losing an observable variable in estimation and this reduces the information I can have in likelihood function so my estimation may be affected by this. What I get form you is that even I can’t use all of information in likelihood function, my estimation would be fine. Is this correct.

Yes, this is correct. Your estimation should be fine.