I have formulated a DSGE model and it has capital accumulation with both capital and investment as state variables, and it is perturbed by an marginal efficiency of investment shock in capital accumulation equation. I am wondering that should I choose investment or capital to be observable/link with an observable? which is better at helping identifying marginal efficiency of investment shock? option 1: choose investment state variable to be associated with real investment observable data/flow observable variable. option 2: choose capital state variable to be associated with gross capital formation observable data/ stock variable, which option sounds reasonable in helping identifying marginal efficiency of investment shock? I have seen literature choose investment state variable as observable variable instead of choosing capital state variable as observable variable? why investment data is preferable over capital data?
Thank you very much and look forward to hearing from you.
In the presence of an MEI shock, you would like to observe both variables, as it allows backing out the MEI shock perfectly. That being said, you typically never observe the capital stock consistent with an MEI shock. Capital stocks are rarely available at a quarterly level and if they are, they are usually computed from investment flows using a perpetual inventory method that assumes no MEI shocks are present. For that reason, you usually can only use investment, which is at least somewhat precisely measured.