Can capital share in production and capital depreciation rate be estimated instead of calibrating them

Dear Johannes,
First thank you for your previous guidance, I am grateful.
I have modelled a DSGE model with state owned firms and private firms, where state owned firms engage in heavy industry and private firms engage in light industry. I have two questions.

  1. In the estimation of firms’ production function, can capital share alpha be estimated instead of calibrated?
    production function Y=A*K^alpha *L^(1-alpha)
    where Y is production, A is technology, K is capital, L is labor, alpha is capital share, (1-alpha) is labor share.
  2. In the estimation of firms capital accumulation, can capital depreciation rate delta be estimated instead of calibrated?
    capital accumulation K=(1-delta)K(-1)+I,
    where K is capital, delta is capital depreciation rate, I is investment.
    Thank you and look forward to hearing from you.
    Best regards,

Yes, you can typically estimate those parameters. However, they are typically best identifed by the average capital share and the average investment to capital ratio. SO calibrating them is often straightforward. If you don’t have those data, you should check identification.