Can output, investment, consumption and government spending all be included as observables

[Jesse]

Dear Johannes,
First thank you for your previous guidance, I am grateful.
I have a question regarding estimating DSGE models, in my DSGE model, I would like to include output, consumption, investment and government spending all as observable variables, however, theoretically, output should be a linear combination of consumption, investment and government spending. Although all these variables are log differenced/growth rates, I am wondering will there be any problems like perfectly linearity among observables if I include output, consumption, investment and government spending growth rates simultaneously as observables for estimating DSGE models?
Thank you and look forward to hearing from you.
Best regards,
Jesse

[jpfeifer]

See

Cannot have more observed variables than shocks?

Yes, that is true. The problem is known as “stochastic singularity”. The problem is that in a linear model if you have fewer shocks than observables, there will be an exact linear combination implied between observables. That in turn means that the density of observing those variables is either 1 (the exact linear combination in the model holds in the data; rarely the case) or 0 (the exact linear combination does not hold; the typical case). As you can imagine with a log density of minus infinit…

[Jesse]

Thank you for your helpful guidance!