Estimating the rental rate of capital from data Take the classic optimization problem of the neo-classical firm:

\begin{equation}
 \begin{array}{*2{&gt;{\displaystyle}r}}
 \mbox{maximize (over $K, L$)} &amp; 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.
Time series on rental price of capital can be estimated using $$r=\frac{P_k}{P}(i-inf+\delta)$$
here, $P_k$ is the price of capital goods (price index for capital goods), $P$ is a deflator, $i$ is nominal interest rate, $inf$ is an inflation rate and $\delta$ is depreciation rate of physical capital stock.