Data treatment for calibration PIM

Hi everyone

When using the PIM method to calculate capital depreciation rates in a model with no population growth, is the data used divided by the population? For example, in two periods, I use the following: gross fixed capital formation, average consumption of fixed capital, and gross domestic product,

Data = \{Y_{2019}, Y_{2020}, I_{2019}, I_{2020}, CFK\}
K_{2020} = (1 - \delta)*K_{2019} + I_{2019}
K_{2021} = (1 - \delta)*K_{2020} + I_{2020}
\frac{1}{2} ( \frac{K_{2019}}{Y_{2019}} + \frac{K_{2020}}{Y_{2020}}) = \frac{K_{2019}}{Y_{2019}}
\frac{1}{2} ( \frac{\delta K_{2019}}{Y_{2019}} + \frac{\delta K_{2020}}{Y_{2020}}) = CFK

unknown variables = \{ K_{2019}, K_{2020}, K_{2021}, \delta \}

Should the data be per capita?

As always, it depends on what you are trying to do. Here, the question is what delta is supposed to be. If K_{t+1}=(1-\delta)K_ {t}+I_t
is supposed to capture the technical relationship in the data, then that is the way to go. Population growth usually matters when working with intensive form variables in the model. Take the Solow model. You end up with
(1+n)k_{t+1}=(1-\delta)k_ {t}+i_t
where now everything is per capita.