<p><span class="math-container">$$i \approx r+ \pi$$</span></p>
<p>where <span class="math-container">$i$</span> is nominal interest rate, <span class="math-container">$r$</span> real interest rate and <span class="math-container">$\pi$</span> inflation rate/expected inflation is an approximation coming from identity:</p>
<p><span class="math-container">$$(1+i)=(1+r)(1+\pi)$$</span></p>
<p>The real interest rate is inflation adjusted interest rate so <span class="math-container">$r \approx i - \pi$</span> and as any identity you can algebraically manipulate it.</p>
<p>This is equivalent of real GDP given as:</p>
<p><span class="math-container">$$rGDP=GDP/P$$</span></p>
<p>where <span class="math-container">$rGDP$</span> is real GDP, GDP nominal GDP and <span class="math-container">$P$</span> price level/deflator. These are relationships that hold by construction.</p>
<p>Trivially if you somehow know future real interest rate and nominal interest rate you can not just forecasts inflation you can literally just state exactly what the inflation is.  <span class="math-container">$i \approx r + \pi$</span> is completely deterministic mechanical relationship, if you know that at time <span class="math-container">$t$</span>; <span class="math-container">$i$</span> is 2% and <span class="math-container">$r$</span> is 1% inflation has to be 1%.</p>
<p>So you can use the Fisher identity to figure out what current inflation/expected inflation is, but for that you need to know current <span class="math-container">$i$</span> and <span class="math-container">$r$</span>, or alternatively if you want to know what future inflation is, you need to know future <span class="math-container">$i$</span> and future <span class="math-container">$r$</span> and then determine inflation from that.</p>
<p>If you want to forecast what inflation will be <em>in the future</em>, based on <em>the current</em> interest rate you have to have some model where:</p>
<p><span class="math-container">$$\pi_{t+1}=f(i_t)$$</span></p>
<p>Having model where <span class="math-container">$i_t= r_t+ \pi_t$</span> does not help much because then to know <span class="math-container">$\pi_{t+1}$</span> you need to first forecast <span class="math-container">$i_{t+1}$</span> and <span class="math-container">$r_{t+1}$</span> so you need to build a separate forecasting model that can simultaneously do that.</p>
<blockquote>
<p>Would this also hold for say, nominal stock returns or dividend yields, since they haven't been adjusted for inflation, their nominal values should already include a reflection of future inflation?</p>
</blockquote>
<p>In context of adjusting for inflation the values do not reflect future inflation. To be clear of course stock prices depend on future inflation but if we talk about relationship between nominal and real variables such <span class="math-container">$i \approx r+\pi$</span> or real and nominal price of a stock they do not tell you what the future inflation is. <span class="math-container">$\pi$</span> is the current inflation, or the current inflation expectation since inflation cannot be measured in real time. <span class="math-container">$\pi$</span> is the inflation that people expect today not tomorrow.</p>

CC BY-SA 4.0
2022-11-08T12:04:03.063Z
2022-11-08T12:04:03.063Z
1muflon1
<p>Okay, a lil bit stupid question...</p>
<p>Consider the Fisher approximation that,
<em>Nominal interest rate = Real interest rate + Expected inflation rate</em>,</p>
<p>Does this not posit that the nominal (short-term) interest rate reflects all available information on expected inflation, and thus, can theoretically be used to forecasting future inflation?
Or am I tripping?</p>
<p>Would this also hold for say, nominal stock returns or dividend yields, since they haven't been adjusted for inflation, their nominal values should already include a reflection of future inflation?</p>
<p>Please help me un-trip, thanks!!</p>

CC BY-SA 4.0
2022-11-08T09:37:30.273Z
"*Nominal interest rate = Real interest rate + Expected inflation rate*" Sorry, but how does it follow from this that the nominal interest rate determines expected inflation? Seems like there are two variables on the right site, and nominal interest rate only determines their sum?
Giskard
CC BY-SA 4.0
2022-11-08T11:24:51.213Z
As Giskard says, you'd need also the real interest rate to extract inflation expectations. If you are interested in inflation expectations there are other ways of getting them.
BrsG
<macroeconomics><inflation><interest-rate><forecasting>
Nominal financial variables reflect all available information on inflation?
YaNo
# Nominal financial variables reflect all available information on inflation?

(Asked by: username_0 on 2022-11-08)

Okay, a lil bit stupid question...

Consider the Fisher approximation that,
*Nominal interest rate = Real interest rate + Expected inflation rate*,

Does this not posit that the nominal (short-term) interest rate reflects all available information on expected inflation, and thus, can theoretically be used to forecasting future inflation?
Or am I tripping?

Would this also hold for say, nominal stock returns or dividend yields, since they haven't been adjusted for inflation, their nominal values should already include a reflection of future inflation?

Please help me un-trip, thanks!!

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

> **Comments:**
> **username_1**: "*Nominal interest rate = Real interest rate + Expected inflation rate*" Sorry, but how does it follow from this that the nominal interest rate determines expected inflation? Seems like there are two variables on the right site, and nominal interest rate only determines their sum?  
> **username_2**: As username_1 says, you'd need also the real interest rate to extract inflation expectations. If you are interested in inflation expectations there are other ways of getting them.  

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## 1 answers

### Answer by username_3 on 2022-11-08. Score: 0

$$i \approx r+ \pi$$

where $i$ is nominal interest rate, $r$ real interest rate and $\pi$ inflation rate/expected inflation is an approximation coming from identity:

$$(1+i)=(1+r)(1+\pi)$$

The real interest rate is inflation adjusted interest rate so $r \approx i - \pi$ and as any identity you can algebraically manipulate it.

This is equivalent of real GDP given as:

$$rGDP=GDP/P$$

where $rGDP$ is real GDP, GDP nominal GDP and $P$ price level/deflator. These are relationships that hold by construction.

Trivially if you somehow know future real interest rate and nominal interest rate you can not just forecasts inflation you can literally just state exactly what the inflation is. $i \approx r + \pi$ is completely deterministic mechanical relationship, if you know that at time $t$; $i$ is 2% and $r$ is 1% inflation has to be 1%.

So you can use the Fisher identity to figure out what current inflation/expected inflation is, but for that you need to know current $i$ and $r$, or alternatively if you want to know what future inflation is, you need to know future $i$ and future $r$ and then determine inflation from that.

If you want to forecast what inflation will be *in the future*, based on *the current* interest rate you have to have some model where:

$$\pi\_{t+1}=f(i\_t)$$

Having model where $i\_t= r\_t+ \pi\_t$ does not help much because then to know $\pi\_{t+1}$ you need to first forecast $i\_{t+1}$ and $r\_{t+1}$ so you need to build a separate forecasting model that can simultaneously do that.

> Would this also hold for say, nominal stock returns or dividend yields, since they haven't been adjusted for inflation, their nominal values should already include a reflection of future inflation?

In context of adjusting for inflation the values do not reflect future inflation. To be clear of course stock prices depend on future inflation but if we talk about relationship between nominal and real variables such $i \approx r+\pi$ or real and nominal price of a stock they do not tell you what the future inflation is. $\pi$ is the current inflation, or the current inflation expectation since inflation cannot be measured in real time. $\pi$ is the inflation that people expect today not tomorrow.


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