<p>The existing answer to this question makes a valid point about endogeneity, but I am choosing not to address it because the question refers to <em>correlation</em> and nothing more.</p>
<p>There are two reasons why we might expect interest rates to be correlated to inflation:</p>
<ol>
<li>The Fisher Effect.</li>
</ol>
<p>This has already been mentioned. If, as I think seems reasonable, we believe that the long-run real interest rate is determined by the supply side, then there must be a long-run positive relationship between the <em>nominal</em> interest rate and the level of inflation. Sustained inflation must ultimately result in a higher nominal interest rate, cp.</p>
<ol start="2">
<li>Anticipation.</li>
</ol>
<p>Depending on how you measure inflation, it is possible that the Central Bank has access to some indicators which might enable it to predict future inflation. This would mean that a forward-looking Central Bank could increase rates <em>before</em> they observe an increase in inflation (and vv), because they know it is coming.</p>
<p>Indeed, since monetary policy changes take time to have an effect, a Central Bank would need to make their decisions ahead of the phenomenon they were trying to affect.</p>
<p>It might seem implausible to think that a Central Bank can know how inflation will develop, but there are <em>some</em> leading indicators of both output and inflation (for example, certain kinds of input prices) which might enable a Central Bank to predict future shocks.</p>
<p>Neither of these arguments, of course, say anything about the efficacy of monetary policy. To assess that you need a causal (or at least, a structural) assessment of the relationship, which is not what you asked about nor what I have addressed.</p>

CC BY-SA 4.0
2024-08-11T16:01:08.720Z
2024-08-11T16:01:08.720Z
matthewoulton
<p>The answer is that what you are getting is bias from naive regression and there isn't a positive relationship, careful empirical studies using appropriate models show the relationship is negative. If you are running simple naive regression you will get biased results due non-stationarity of the series and endogeneity. Hence your positive correlation is caused by bias and is no indication of what the relationship between the two variables is.</p>
<p>To examine relationship between interest rates and inflation you need some model that can handle both endogeneity, and series being non-stationary and in this case actually not just non-stationary but also cointegrated. An one alternative is to run Vector Error Correction (VEC) Model. VEC similarly to VAR solves endogeneity problem and it allows for non-stationary and cointegrated variables  (see Verbeek A Guide to Modern Econometrics 3rd ed ch 9.5).</p>
<p>Empirical studies such as <a href="https://www.sciencedirect.com/science/article/pii/S1042444X01000305?casa_token=774Q5pusuv8AAAAA:dUimb1c2-LP0UK4fV4zdIKyOOLe1UWM6cyf6oul3-M6uCV1dv-3k80oXsyGMOJMBqWcfkJ7Y7z0" rel="nofollow noreferrer">Booth &amp; Ciner (2001)</a> show that there is a negative relationship between interest rates and inflation around the world:</p>
<p><a href="https://i.sstatic.net/DD1ih.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DD1ih.png" alt="enter image description here" /></a></p>
<p>If there would be Fisher effect present the relationship would be positive in the cointegrated models above. In naive regression you just get positive results because of endogeneity and stochastic trends that create spurious correlation.</p>

CC BY-SA 4.0
2022-07-26T00:04:14.470Z
I used a vecm model to check for cointegration and at the 1% critical levels there is no case for rejecting stationarity, but there is at the 5%. As far as I understand it, it's obviously up to me how much precision I need. Can you explain where you see a negative relationship in the Booth & Ciner study? I only see negative std.
PostScriptum
CC BY-SA 4.0
2022-07-26T01:49:24.960Z
@PostScriptum VECM is not test for stationarity, I am not sure how you used it to test for stationarity. Std here is not standard deviation, btw standard deviation cannot even be negative that’s impossible, std here stands for standardized, in VECM you always have to standardize your coefficients otherwise they are hard to interpret
1muflon1
CC BY-SA 4.0
2022-07-27T05:51:16.237Z
Part of the process of creating a vecm model is testing for stationarity, because if it's not present it's just a var model then. I did this in r with the ca.jo function. Yeah ok standard deviation can't be negative, what would the -1.5 for Belgium mean?
PostScriptum
CC BY-SA 4.0
2022-07-27T11:50:09.037Z
@PostScriptum but ca.jo function does not test for stationarity. The -1.5 is the standardized effect between inflation and interest rates
1muflon1
CC BY-SA 4.0
2022-07-28T16:21:45.473Z
I meant the cointegration test.
PostScriptum
CC BY-SA 4.0
2022-07-28T16:23:31.920Z
@PostScriptum oh ok, but the Johansen cointegration test (which is what you get from ca.jo) will be biased if the variables are not integrated of the same order. You first have to check that using some auxiliary unit root tests
1muflon1
CC BY-SA 4.0
2022-07-21T10:53:48.820Z
2022-07-21T11:11:32.433Z
2022-07-21T11:11:32.433Z
1muflon1
<p>I regressed quarterly CPI on lagged quarterly (from 1 to 8 quarters) 10-year Treasuries, and found that with data from roughly 1990, the coefficient of the lagged rates tends to be positive. This implies that as interest rates rise, inflation also rises. Excluding the earlier data and using only more recent data results in a negative coefficient. I thought this might be due to the ineffective use of interest rates following the oil crisis in the 70s, but the 80s also follow this trend.</p>
<p>P.S. Using the Federal Funds Rate results in a positive coefficient no matter what.</p>

CC BY-SA 4.0
2022-07-20T17:37:46.907Z
https://en.wikipedia.org/wiki/Fisher_effect
H2ONaCl
CC BY-SA 4.0
2022-07-20T18:47:44.190Z
CPI is not inflation but price level, looks like a unit root spurious correlation
WilliamT
CC BY-SA 4.0
2022-07-20T19:43:22.007Z
Could you please provide links to the data you use and minimal working example?
1muflon1
<inflation>
Why is the Correlation between Interest Rates and Inflation positive?
PostScriptum
# Why is the Correlation between Interest Rates and Inflation positive?

(Asked by: username_0 on 2022-07-20)

I regressed quarterly CPI on lagged quarterly (from 1 to 8 quarters) 10-year Treasuries, and found that with data from roughly 1990, the coefficient of the lagged rates tends to be positive. This implies that as interest rates rise, inflation also rises. Excluding the earlier data and using only more recent data results in a negative coefficient. I thought this might be due to the ineffective use of interest rates following the oil crisis in the 70s, but the 80s also follow this trend.

P.S. Using the Federal Funds Rate results in a positive coefficient no matter what.

**Tags:** inflation
> **Comments:**
> **username_1**: https://en.wikipedia.org/wiki/Fisher_effect  
> **username_2**: CPI is not inflation but price level, looks like a unit root spurious correlation  
> **username_3**: Could you please provide links to the data you use and minimal working example?  

---

## 2 answers

### Answer by username_4 on 2024-08-11. Score: 0

The existing answer to this question makes a valid point about endogeneity, but I am choosing not to address it because the question refers to *correlation* and nothing more.

There are two reasons why we might expect interest rates to be correlated to inflation:

1. The Fisher Effect.

This has already been mentioned. If, as I think seems reasonable, we believe that the long-run real interest rate is determined by the supply side, then there must be a long-run positive relationship between the *nominal* interest rate and the level of inflation. Sustained inflation must ultimately result in a higher nominal interest rate, cp.

2. Anticipation.

Depending on how you measure inflation, it is possible that the Central Bank has access to some indicators which might enable it to predict future inflation. This would mean that a forward-looking Central Bank could increase rates *before* they observe an increase in inflation (and vv), because they know it is coming.

Indeed, since monetary policy changes take time to have an effect, a Central Bank would need to make their decisions ahead of the phenomenon they were trying to affect.

It might seem implausible to think that a Central Bank can know how inflation will develop, but there are *some* leading indicators of both output and inflation (for example, certain kinds of input prices) which might enable a Central Bank to predict future shocks.

Neither of these arguments, of course, say anything about the efficacy of monetary policy. To assess that you need a causal (or at least, a structural) assessment of the relationship, which is not what you asked about nor what I have addressed.


---

### Answer by username_3 on 2022-07-21. Score: 0

The answer is that what you are getting is bias from naive regression and there isn't a positive relationship, careful empirical studies using appropriate models show the relationship is negative. If you are running simple naive regression you will get biased results due non-stationarity of the series and endogeneity. Hence your positive correlation is caused by bias and is no indication of what the relationship between the two variables is.

To examine relationship between interest rates and inflation you need some model that can handle both endogeneity, and series being non-stationary and in this case actually not just non-stationary but also cointegrated. An one alternative is to run Vector Error Correction (VEC) Model. VEC similarly to VAR solves endogeneity problem and it allows for non-stationary and cointegrated variables (see Verbeek A Guide to Modern Econometrics 3rd ed ch 9.5).

Empirical studies such as [Booth & Ciner (2001)](https://www.sciencedirect.com/science/article/pii/S1042444X01000305?casa_token=774Q5pusuv8AAAAA:dUimb1c2-LP0UK4fV4zdIKyOOLe1UWM6cyf6oul3-M6uCV1dv-3k80oXsyGMOJMBqWcfkJ7Y7z0) show that there is a negative relationship between interest rates and inflation around the world:

[![enter image description here](https://i.sstatic.net/DD1ih.png)](https://i.sstatic.net/DD1ih.png)

If there would be Fisher effect present the relationship would be positive in the cointegrated models above. In naive regression you just get positive results because of endogeneity and stochastic trends that create spurious correlation.

> **Comments:**
> **username_0**: I used a vecm model to check for cointegration and at the 1% critical levels there is no case for rejecting stationarity, but there is at the 5%. As far as I understand it, it's obviously up to me how much precision I need. Can you explain where you see a negative relationship in the Booth & Ciner study? I only see negative std.  
> **username_3**: @PostScriptum VECM is not test for stationarity, I am not sure how you used it to test for stationarity. Std here is not standard deviation, btw standard deviation cannot even be negative that’s impossible, std here stands for standardized, in VECM you always have to standardize your coefficients otherwise they are hard to interpret  
> **username_0**: Part of the process of creating a vecm model is testing for stationarity, because if it's not present it's just a var model then. I did this in r with the ca.jo function. Yeah ok standard deviation can't be negative, what would the -1.5 for Belgium mean?  
> **username_3**: @PostScriptum but ca.jo function does not test for stationarity. The -1.5 is the standardized effect between inflation and interest rates  
> **username_0**: I meant the cointegration test.  
> **username_3**: @PostScriptum oh ok, but the Johansen cointegration test (which is what you get from ca.jo) will be biased if the variables are not integrated of the same order. You first have to check that using some auxiliary unit root tests  

---

