# Net of Tax Return on Capital: Definition, Proxy and Data

There is one input factor $k$. The representative firm maximizes profits with respect to employed capital, i.e. \begin{align} \max_k{\pi(k) = f(k)-(r+\tau)k} \end{align} where $f(\cdot)$ is the production function, $r$ the rent of capital and $\tau$ the tax rate to be paid for a unit of capital. The FOC reads \begin{align} \pi'(k)=0\quad\Longleftrightarrow\quad r = f'(k) - \tau \end{align} Now $r$ can be interpreted as a net of tax return on capital for the household (who owns the capital stock).

• Is there a standard proxy for $r$?
• Can you point to empirical literatur, where $r$ is shown for different countries.

Any suggestion is appreciated.

## Edit I

I think I was searching for net national accounts seperated for factor income (firms and workers). I added a picture from the german national stats. I think the last two columns might be appropriate (I hope it's readable).

## Edit II

Found the net return on net capital in AMECO. The variable is named APNDK and you can find a description on page 65 of that list. Is this any good? I don't do empirics.

• I have not read his works but it is my understanding that collecting this kind of empirical data is half of what Thomas Piketty did. On his webpage you will also find data files. piketty.pse.ens.fr/en/publications-en – Giskard Jun 23 '15 at 17:41
• RE: Desnep: My impression is that differences between net and gross returns on capital are not well handled in Piketty's work and data. See for example Jim Hamilton on the subject: econbrowser.com/archives/2014/05/criticisms-of-piketty Re:clueless How do you ideally want to treat depreciation on capital? Integrated into tau? Subtracted from $f(k)$? Abstracted away? – BKay Jun 24 '15 at 12:13
• @BKay Abstracted away I guess. It is a tax competition model and we only care about $\tau$. So we can just set deprecation $\delta=0$. I actually wanna show that rates of return on capital differ across countries. In the classic literature on tax competition they usually assume that capital is perfectly mobile and $r_i = r~\forall i$, where $i=1,2,\ldots$ are countries. My motivation is that in a dynamic model rates of return differ at least in the short run, i.e. $\exists t ~r_i(t)\neq r_j(t)$. – clueless Jun 24 '15 at 15:20