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I am estimating time series for rental price of capital using Hall-Jorgenson method: $$r=\frac{P_k}{P}(i-inf+\delta)$$ here, $r$ is the rental cost of capital, $P_k$ is the price of capital goods (price index for capital goods), $P$ is a deflator, $i$ is nominal interest rate, $inf$ is an inflation rate and $\delta$ is depreciation rate of physical capital stock.

Because inflation rate is high in some periods, the rental cost of capital is negative for these periods; this does not make sense, any little help is welcome!

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In theory there is nothing that is preventing the real interest rate from becoming negative. Making the real interest rate negative by keeping the nominal rate at zero and creating inflation has been the goal of the ECB in the recent past. Once you hit the ZLB there is no other way to further loosen monetary policy. With regard to your work it is probably important to carefully select the inflation rate you're using, but you dont describe this in detail. Depending on your question you might want to consider forward looking measures (i.e.Blue Chip or Greenbook forecasts if you're talking about the US).

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  • $\begingroup$ I used CPI inflation, and the data is for the 1700-1914 period for Britain. $\endgroup$ – london Jul 21 '19 at 14:21
  • $\begingroup$ I see with that time span there arent many different series you can get. I think you should try to tag this question as [economic-history] and describe your data. Then you can hope to find someone to discuss the particular periods when you get negative real rates? $\endgroup$ – Grada Gukovic Jul 21 '19 at 14:31
  • $\begingroup$ I think I sorted the problem, but not sure if the results are convincing; I've reduced the volatility of CPI inflation rate by applying 20-year MAs. $\endgroup$ – london Jul 21 '19 at 16:35
  • $\begingroup$ You could think about your depreciation rate. We used to assume 5% when I did macro. When I think about it the real interest must be very negative with such depreciation before you obtain negative cost of capital. If dont you describe your data on inflation no-one cant give you advice on that. $\endgroup$ – Grada Gukovic Jul 22 '19 at 12:26
  • $\begingroup$ I calculated the depreciation rate using gross capital stock data for the same period. The average depeciation rate is just under 3% $\endgroup$ – london Jul 22 '19 at 22:09

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