Take the classic optimization problem of the neo-classical firm:
\begin{equation} \begin{array}{*2{>{\displaystyle}r}} \mbox{maximize (over $K, L$)} & f(K, L) - RK - WL \end{array} \end{equation}
The first order condition equates the marginal product of capital with the rental rate of capital $R$.
Which raises the question...
How do macroeconomists typically estimate a time series for the rental rate of capital using U.S. data?
(Disclaimer: I don't do macro, but my curiosity has been sparked.)
One approach is to use financial market data to get $R_t$, use another first order condition that the rental rate of capital equals the nominal interest rate plus depreciation (i.e. Hall and Jorgensen). Backing a rental rate out of financial market data is not obvious though! In financial markets, prices vary based upon risk and time.
- time dimension: Long-term rates are typically higher than short-term rates. When macro-economists and macro-models talk about the rental rate of capital, what's the time frame?
- risk dimension: Eg. callable bonds have high yields than non-callable bonds. Debt and equity may have different expected returns based upon risk.
- inflation dimension: A fixed nominal rate is a stochastic real rate depending on realized inflation, and the expected real rate is the nominal rate minus inflation expectations. The real rental rate would add back inflation expectations.
A completely different direction is taken by Casey Mulligan where he sticks entirely with Bureau of Economic Analysis (BEA) data.
I don't follow this literature, and I don't have a sense of the range of approaches that are considered sensible in modern, empirical macro.