Calibration: current prices or constant prices

General DSGE Modeling
1

Hi everyone

I have a question about calibration.Thank you in advance for your help
Suppose that we want to calculate the consumption to production ratio in steady state (C_SS/Y_SS) based on the data:

My question is, which of the following data do we use?

C_SS at current prices/Y_ss at current prices?

Or

C_SS at constant prices/Y_ss at constant prices?

In my opinion, there should be no difference between the two cases mentioned because we have used ratio:

Of course, when we extract data from sources and calculate this ratio based on these data, there is a difference between these two:

C_SS at current prices/Y_ss at current prices = 0.43

C_SS at constant prices/Y_ss at constant prices=0.54

Which of these two ratios should I use ? Which is more correct??

2

The problem is the different goods baskets involved when comparing constant price objects. Please have a look at Remark 9 (An Additional Complication: Chained Indexes) in Pfeifer (2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models".