# Real rental rate of capital

Good morning everyone,

I am trying to build time series on the real rental rate of capital. To do so I apply this formula:
R = Price of investment / Price of value added *(real interest rate - depreciation of capital)

My issus is with the first division. I only have index-form data (base 2014) on investment goods price and value added price. Is it okay if I use the index of price investment goods and the index of value-added price for this formula?

If so, since I’m using indexes, will my rental rate of capital be an index (base 2014) as well?

Best regards

I think it is obvious that you will only get the correct level of the rental rate if you use the correct level for the prices. If you only have an index that will not be assured. The resulting number can be interpreted as an index as well but usually, you would normalize the series to something more common like 100 or 1 in a base year.

Thanks you. But the price of Investment goods, price of value added or even of capital goods are nowhere to be found. That’s why I am using an index for France. Or is there any way to compute it ?

So that means I can use my expression to compute data series on the real rental rate of capital and then normalize to 1 according to a base year value.

Thanks

What are you trying to do with that series? Do you even need to know the level?

Good morning,

I am trying to estimate my elasticities of substitution based on demand équations. Hence, I need time series on the rental rate of capital r, to estimate the elasticity of substitution between capital and labor.

What should I do?

Another question: I have a time series on value added price index base year 2014. Do you have any hint on how to transform in base 1991 the time series of that indice ?

Best regards,

1. Rebasing is easy. Simply divide by the value in the new base year.
2. I was asking because sometimes you can work with growth rates instead of the levels. Then the scaling does not matter.
1. Ok, so I can follow that “So that means I can use my expression to compute data series on the real rental rate of capital and then normalize to 1 according to a base year value” ?

Yes, but I don’t see how that will help you. You still won’t get the correct level.

Yes I know. But most of articles on the estimation of this elasticity are based on indices for the price of Investment goods.

Data on the price of Investment goods or capital goods are very hard to be found. There are no data on oecd data base or the french national statistic institute data base…

Or is there any way to compute it?

I still don’t understand what your problem is. When you are saying

then this suggests that you don’t need the actual level. Then there should be no problem at all.

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Thanks, very much appreciated.

Good afternoon,

I wondered if I could find the rental rate of capital r by using the income distribution identity, meaning:

GDP - capital depreciation = rK + wL -> rK = GDP - capital depreciation - labor compensations -> r= (rK)/K

(GDP - capital depreciations - labor compensation) being the gross operating surplus really

If I use GDP I find an average from 1978 to 2017 of 7 % for France. https://publications.banque-france.fr/sites/default/files/medias/documents/wp-630_0.pdf that refers says so for OECD countries, RoR around 8%
Or is this proxy too vague ?

Thank you

The problem in practice is that the rental rate assumes a competitive rental market. In practice, the can be monopoly rents. Your computation above assigns everything to a rent on capital. If that is what you want, you can do this.

Im assuming capital competitive markets. My model is very aggregated. So the rate of my model corresponds you a rental rate for all sectors. So it should be okayish?

Plus I only need a proxy for the economy. No need for the exact value

Thank you

Then I would try that approach and check whether the results are sensible.