# Capital stock depreciation rate, how to calculate?

I am trying to work out the depreciation rate using the following information, it is an extract from a longer data set on capital stock:

Just wanted to find out what the rate of depreciation is for 2000. I used $K_t=K_{t-1}+I-\delta K_{t-1}$ to calculate the rate of depreciation $\delta$ but I am not satisfied with the result. Any help is appreciated! Note, this is not a homework.

• Just curious, have tried estimating the parameter ($\delta$) by regression? If you look at the recursive estimates you'd see its value through time (i.e including 2000). The approach is similar to estimating tax rate equations, whereby receipts equals the rate times base, and the estimated coefficient on the base is the effective rate. – Graeme Walsh Apr 26 '16 at 18:27
• Just a quick question, do you know of a published paper dealing with effective tax rate estimation? Thanks – london Apr 29 '16 at 14:33

## 1 Answer

Rate of depreciation = depreciation/gross stock in the current year. So 1.7%. Strictly speaking there is no way to calculate depreciation because the timing of capital formation is unknown, but capital begins depreciating as soon as it is formed.

• Yeah, this is the issue, the simple depr/gross stock ratio does not work here. I guess the info is sufficient, but I cannot work out what the rate of depreciation is. The capital formation value is for the whole year. Gross and Net stock values are for end of each year. Can you treat capital formation as an Investment for the given year? – london Mar 27 '16 at 16:10
• That's the only way to do it. There is no exact solution. That is the same way return on equity is calculated, so to be consistent you should use the same method. – D J Sims Mar 27 '16 at 16:24
• The rate of depreciation is about 8% in 2000. I was hoping this can be shown using the above data. – london Mar 27 '16 at 17:08