<p>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 <em>expected</em> inflation.</p>

<p>The real yields On US inflation-linked bonds are currently negative. <a href="https://fred.stlouisfed.org/series/DFII5" rel="nofollow noreferrer">Link to FRED data.</a></p>

<p>There is no mystery to this.</p>

<ul>
<li>Nominal yields are effectively pinned to the expected path of the nominal policy rate.</li>
<li>Inflation rates follow developments in the economy.</li>
<li>There is no law of nature that says that the nominal yield has to be above the rate of inflation.</li>
</ul>

CC BY-SA 4.0
2020-05-25T16:47:55.853Z
2020-05-29T19:16:33.800Z
2020-05-29T19:16:33.800Z
Brian Romanchuk
<p>The Fisher equation does not necessarily implies the chain of causality is from the inflation or nominal interest rate to the real interest rate.</p>

<p>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.</p>

<p>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. </p>

<p><a href="https://i.sstatic.net/J1cXG.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/J1cXG.png" alt="enter image description here"></a></p>

CC BY-SA 4.0
2020-05-25T14:08:23.797Z
" 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.
KarmaPeasant
CC BY-SA 4.0
2020-05-25T14:59:36.697Z
@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
1muflon1
CC BY-SA 4.0
2020-05-25T15:11:41.837Z
"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.
KarmaPeasant
CC BY-SA 4.0
2020-05-25T15:19:15.567Z
@user161005 actually they might because even though that implies they are loosing some money due to the inflation they might still need to make some savings for various reasons (precautionary savings etc) and  it can also be part of strategy that minimizes losses. There was nice post here on SE why people still invest even with negative interest rates I will try to find it and give you link to it but part of the explanation included that also some institutions are forced to invest let’s say safe bonds even at negative interest rate and they can still be part of risk hedging and so on
1muflon1
CC BY-SA 4.0
2020-05-25T15:22:45.867Z
I understand logic of "minimizing losses" when all options lead to losses. What I don't understand is why private investors won't just buy gold or loan their money to foreigners instead of giving such bad loans?
KarmaPeasant
CC BY-SA 4.0
2020-05-25T15:28:28.007Z
@user161005 this would be an interesting question in itself  that I don’t think I can answer fully in a comment but problem is that gold is a commodity - commodities fluctuate in value due to various reasons. For example, if there would be some be development that would allow synthetic gold to be created the same way as now you can diamonds it might easily set the price of gold to plummet. Also gold is not very liquid and liquidity is a good thing in itself I can’t imagine anyone living with having all savings in illiquid assets just from practical reasons and so forth
1muflon1
CC BY-SA 4.0
2020-05-25T15:32:32.067Z
When it comes to bonds t bills etc again they are not very liquid - although more than gold. For better or worse in many countries you might not be able to directly access bond markets - many places have regulations that mean ordinary people have to go through banks/funds or other intermediaries - times where you as a private person could go to bond exchange and trade are in most places things of the past. You might still be able to buy bonds directly from government but without access to bond markets you have to way patiently for them to expire to get your money back so they become illiquid
1muflon1
CC BY-SA 4.0
2020-05-25T15:34:56.790Z
Do you mean that it's often very problematic to access foreign bond markets for private non-instituional agents? Did I get it right?
KarmaPeasant
CC BY-SA 4.0
2020-05-25T16:08:29.773Z
@user161005 yes for example in NL where I live ordinary person can access bond market pretty much only through special investment bank account and unless you pay for expensive investment accounts your trades might take up to week to execute and NL is in this regard still better than other countries in Europe. Also that few days up to one week in NL might not seem as much but if you are in dire need of liquidity it is important.
1muflon1
CC BY-SA 4.0
2020-05-25T11:59:00.783Z
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?
KarmaPeasant
CC BY-SA 4.0
2020-05-25T13:00:44.030Z
@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).
1muflon1
CC BY-SA 4.0
2020-05-25T11:50:52.640Z
2020-05-25T12:47:15.917Z
2020-05-25T12:47:15.917Z
1muflon1
<p>According to Fisher's equation,</p>

<p>Real interest rate=Nominal interest rate - <strong>expected</strong> inflation rate</p>

<p>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 <strong>expected</strong>.</p>

<p>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 <strong>lower</strong> than inflation. BUT Fisher's equation uses only <strong>expected</strong> inflation as its argument, not <strong>actual</strong> inflation. We don't have any right to supply Fisher's equation with <strong>unexpected actual</strong> inflation.</p>

CC BY-SA 4.0
2020-05-25T16:48:39.677Z
This is not a question. It’s a n assertion of an obviously incorrect statement.
Brian Romanchuk
CC BY-SA 4.0
2020-05-25T11:40:40.360Z
"*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.
Giskard
CC BY-SA 4.0
2020-05-25T11:49:07.483Z
@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?
KarmaPeasant
CC BY-SA 4.0
2020-05-25T12:03:02.030Z
What is the creditor's alternative? Not lend money and have inflation "eat up" more of her funds?
Giskard
CC BY-SA 4.0
2020-05-25T12:13:10.347Z
@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.
KarmaPeasant
CC BY-SA 4.0
2020-05-25T13:05:18.657Z
By assuming that such investment possibilities exist you are assuming that the real interest rate is positive.
Giskard
CC BY-SA 4.0
2020-05-25T13:55:36.417Z
@Giskard I don't see how it follows, can you elaborate?
KarmaPeasant
<macroeconomics><inflation><interest-rate><debt>
How can we get negative **real** interest rate?
KarmaPeasant
# How can we get negative **real** interest rate?

(Asked by: username_0 on 2020-05-25)

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.

**Tags:** macroeconomics, inflation, interest-rate, debt

> **Comments:**
> **username_2**: "*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.  
> **username_0**: @username_2 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?  
> **username_2**: What is the creditor's alternative? Not lend money and have inflation "eat up" more of her funds?  
> **username_0**: @username_2 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.  
> **username_2**: By assuming that such investment possibilities exist you are assuming that the real interest rate is positive.  
> **username_0**: @username_2 I don't see how it follows, can you elaborate?  
> **username_1**: This is not a question. It’s a n assertion of an obviously incorrect statement.  

---

## 2 answers

### Answer by username_1 on 2020-05-25. Score: 3

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.](https://fred.stlouisfed.org/series/DFII5)

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.


---

### Answer by username_3 on 2020-05-25. Score: 2

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](https://i.sstatic.net/J1cXG.png)](https://i.sstatic.net/J1cXG.png)

> **Comments:**
> **username_0**: 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?  
> **username_3**: @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).  
> **username_0**: " 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.  
> **username_3**: @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  
> **username_0**: "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.  
> **username_3**: @user161005 actually they might because even though that implies they are loosing some money due to the inflation they might still need to make some savings for various reasons (precautionary savings etc) and  it can also be part of strategy that minimizes losses. There was nice post here on SE why people still invest even with negative interest rates I will try to find it and give you link to it but part of the explanation included that also some institutions are forced to invest let’s say safe bonds even at negative interest rate and they can still be part of risk hedging and so on  
> **username_0**: I understand logic of "minimizing losses" when all options lead to losses. What I don't understand is why private investors won't just buy gold or loan their money to foreigners instead of giving such bad loans?  
> **username_3**: @user161005 this would be an interesting question in itself  that I don’t think I can answer fully in a comment but problem is that gold is a commodity - commodities fluctuate in value due to various reasons. For example, if there would be some be development that would allow synthetic gold to be created the same way as now you can diamonds it might easily set the price of gold to plummet. Also gold is not very liquid and liquidity is a good thing in itself I can’t imagine anyone living with having all savings in illiquid assets just from practical reasons and so forth  
> **username_3**: When it comes to bonds t bills etc again they are not very liquid - although more than gold. For better or worse in many countries you might not be able to directly access bond markets - many places have regulations that mean ordinary people have to go through banks/funds or other intermediaries - times where you as a private person could go to bond exchange and trade are in most places things of the past. You might still be able to buy bonds directly from government but without access to bond markets you have to way patiently for them to expire to get your money back so they become illiquid  
> **username_0**: Do you mean that it's often very problematic to access foreign bond markets for private non-instituional agents? Did I get it right?  
> **username_3**: @user161005 yes for example in NL where I live ordinary person can access bond market pretty much only through special investment bank account and unless you pay for expensive investment accounts your trades might take up to week to execute and NL is in this regard still better than other countries in Europe. Also that few days up to one week in NL might not seem as much but if you are in dire need of liquidity it is important.  

---

