# Capital and output ratio estimation

Dear @wmutschl, in your video “RBC Baseline Model in Dynare: Simple vs Advanced Calibration using Modularization and Changing Types” (https://www.youtube.com/watch?v=HRpynlbZBzM&t=300s), you state that the average capital productivity (K/Y) is roughly between 9 and 10 (min 5:30). Can you elaborate on that? Is that an estimation originated from the steady state conditions of a basic rbc model or does the number come from data?

If I go to fred and I compute Capital Stock at Constant National Prices for United States/Real Gross Domestic Product, I obtain numbers between 3 and 4 (for 1990 to 2019) for the United States. Following the same procedure, if I pick Germany, France and Australia, I have a ratio between 24-28, 27-30 and 10-11 respectively.

On the other hand, in the pdf (https://pages.stern.nyu.edu/~dbackus/BCH/inputs/pwt_ky_ratios.pdf), you have rather consistent ratios for 11 countries between 1 and 4.

Finally, just as a clarification, when calibrating rbc models, is it standard practice to set depreciation delta as \delta=\frac{\bar{I}}{\bar{K}}=\frac{\bar{I}/\bar{K}}{\bar{K}/\bar{Y}} where the ratios are empirically found rather than setting \delta to the NIPA capital consumption rate?

Good point, one should probably indeed use a different calibration target here, I don’t remember where I got the 9 between 10 and have not given much thought to this
Do you know what the original calibration of Kydland and Prescott (1982) or King and Rebelo (1999) implies for K/Y in steady-state?

Regarding the depreciation rate: yes, that is a steady-state relationship of the model. So if you take calibration serious and you have data for long-run averages, then this should be the value for the depreciation rate.

You need to be careful about the frequency of the model. K/Y divides a stock by a flow. The quarterly flow variable is roughly one fourth of the yearly one. PWT is annual, which explains the lower values you mention above.

Empirically, computing capital stocks is hard because we don’t have good data. The perpetual inventory method only goes some way to solving that issue and it very much depends on the value you assign for depreciation. Thus, it’s often easier to just pick a number for the depreciation rate.

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Thank you @wmutschl for your answer! You are right, Kydland and Prescott (1982) does the distinction. Steady-state capital to annual output ratio of 2.4. Inventories are about one-fourth of annual GNP. So k/y = 10, y was divided by 4. Now I understand the numbers.

@jpfeifer, to confirm, if I have a variable, quarterly displayed, but with a yearly basis (such as GDP) I have to divide it by four, right? If I have aggregate quarterly banking data (balance sheet and income statement items) and take interest income, the said variable is already in quarterly terms so it must be kept as it is, but total liabilities need to be divided by 4 because it is total liabilities of the whole year, right?

Sorry, but I am confused by your phrasing of the question. Stocks are invariant to the frequency of the model but flows are not. If your data is already quarterly and you are setting up a quarterly model, then you can use the ratios as in the data. The problem arises when you have a stock-flow ratio from annual data but you are working with a quarterly model.