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According to Fisher's equation,

Real interest rate=Nominal interest rate - expected inflation rate

So, how can we get negative real interest rate? I'm in doubts. On one hand, purely from algebraic point of view it seems that expected inflation rate must be higher than nominal interest rate. BUT, I know that expectations of such high inflation would cause the nominal interest rate to adjust accordingly, to be higher than expected inflation rate. So such situation would appear to be impossible when inflation rate is expected.

On the other hand, replacing "expected" with "actual" turns the tables. If high inflation rate caught us by suprise it's totally possible for nominal interest rate to be lower than inflation. BUT Fisher's equation uses only expected inflation as its argument, not actual inflation. We don't have any right to supply Fisher's equation with unexpected actual inflation.

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    $\begingroup$ "I know that expectations of such high inflation would cause the nominal interest rate to adjust accordingly, to be higher than expected inflation rate." How do you "know" this? Perhaps you have made some questionable assumptions. $\endgroup$ – Giskard May 25 at 11:40
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    $\begingroup$ @Giskard My reasoning is simple. What kind of a sane creditor will lend you money when inflation is expected to be so high, that it will "eat up" all gains at the current nominal interest rate? Is there something wrong with such reasoning? $\endgroup$ – user161005 May 25 at 11:49
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    $\begingroup$ What is the creditor's alternative? Not lend money and have inflation "eat up" more of her funds? $\endgroup$ – Giskard May 25 at 12:03
  • $\begingroup$ @Giskard The creditor can convert their money into foreign currency and loan their money in a country with better conditions. The creditor can buy something that is inflation-prone, like gold. $\endgroup$ – user161005 May 25 at 12:13
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    $\begingroup$ By assuming that such investment possibilities exist you are assuming that the real interest rate is positive. $\endgroup$ – Giskard May 25 at 13:05
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There is a market for inflation-linked bonds. The quoted yield on the bonds is the equivalent of a real yield, with the inflation rate corresponding to expected inflation.

The real yields On US inflation-linked bonds are currently negative. Link to FRED data.

There is no mystery to this.

  • Nominal yields are effectively pinned to the expected path of the nominal policy rate.
  • Inflation rates follow developments in the economy.
  • There is no law of nature that says that the nominal yield has to be above the rate of inflation.
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The Fisher equation does not necessarily implies the chain of causality is from the inflation or nominal interest rate to the real interest rate.

The real interest rate is given by the intersection of the IS LM curve - as shown on the diagram below. The real interest rate depends on the availability of savings. The same way as recently the futures oil price became negative due to excess amount of oil and not enough space to store it, the real interest rate might became negative when there is excess saving in the market.

For example, in the picture below its not the real interest rate that is changed by inflation and nominal interest rate - rather given what the real interest rate is and given what nominal interest rate central banks set inflation adjusts (at least thats what is happening in situations where economy is at zero lower bound above it the situation is more complex). Real interest rate can be be affected by central banks as well but it is quite difficult to actually shift it. Usually the real interest rate is the one determined by macroeconomic situation and central banks adjust the nominal interest rate in a way to hit their target inflation.

enter image description here

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  • $\begingroup$ Are you saying that nominal interest rate can be lower than expected inflation rate if there is too much savings on the loanable funds market? $\endgroup$ – user161005 May 25 at 11:59
  • $\begingroup$ @user161005 not exactly, rather what the fisher equation is saying that the nominal interest rate is the real interest with added inflation it. Also note that its also not correct to say its nominal interest rate - inflation as it is nominal interest rate minus change of the price level (which usually is increasing so many people call it inflation but it could also be decreasing which would give you deflation). $\endgroup$ – 1muflon1 May 25 at 13:00
  • $\begingroup$ " real interest rate might became negative when there is excess saving in the market." But can nominal interest rate be lower than expected inflation? You didn't answer this part. $\endgroup$ – user161005 May 25 at 14:08
  • $\begingroup$ @user161005 yes it can there is nothing that would prevent that in principle for example r interest rate of -10% is consistent with nominal interest rate 0 and 10% inflation. However, you are right that when r is positive usually nominal interest rate is bigger than inflation since i = r + pi $\endgroup$ – 1muflon1 May 25 at 14:59
  • $\begingroup$ "there is nothing that would prevent that in principle" From purely algebraic point - yes. But I'm asking about real life. No sane creditor will lend at nominal interest rate that is lower than expected inflation. If people won't take loan with such nominal interest rate, then the creditor can convert money into another currency and lend them to foreigners. Or just buy gold to preserve their wealth. $\endgroup$ – user161005 May 25 at 15:11

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