IRF Return to capital is decreasing?!

Dear all,

I try to look at the consequences of aid shocks (foreign transfers) in a RBC framework. In one of the scenerios the government uses the additional aid to reduce the taxes on capital. This leaves the households with more income, and so consume more and invest more. This leads to an increase in output. My idea is that is output increases the marginal producivities of capital and labor should increase as well. And yes wages go up but the price of capital ® decreases and continue to decrease while output is increasing. Does anyone have an explanation for that?

If tried to look for papers that focus on the return to capital after a shock but I can’t really seem to find anything that pushes me in the right direction.

Thank you!

Taxes create a wedge between the marginal rate of substitution and the marginal product of labor. If you now decrease capital taxes, that wedge decreases as well. Thus, you need to look at the correct after-tax measure. See e.g. Figure 2 of Born/Peter/Pfeifer (2013): Fiscal News and macroeconomic volatility,

Thank you! That was exactly what I needed!

Could I ask you one follow up question? I also have a scenario where the taxes are fixed (set as parameters) and where the households receive the aid as a lump sum transfer: their income goes up. They can use this for consumption or investment. Both IRF functions show an increase in these variables at impact. This leads to an increase in capital the next period and so pushes up output. Than I am stuck with the same problem: return on capital goes down.

As the tax rate now doesn’t change, the wedge between the marginal rate of substitution and the marginal product also shouldn’t change, right? Then how can I explain by decrease in the return on capital?

Production functions feature decreasing marginal returns to the individual factors. If you have a pure wealth effect, labor will go down and capital up. Both will depress the marginal product.

Of course! Many thanks! Again.