<p>I am reading this famous paper 'Taylor’s Rule and the Fed: 1970–1997', and there is no check for stationarity, non-stationarity, integration or cointegration of the data, but the author just use OLS. When is that OK? I realized other studies estimating Taylor rule also do not transform the data in any way. Is it because interest rate, inflation, output gap appears stationary? The federal funds rate in levels fails ADF test when I checked, but it seems it does not matter much for Taylor rule estimation. Is that correct? When is violating stationarity or cointegration assumption ok?</p>

CC BY-SA 4.0
2021-09-11T15:43:51.437Z
Hi: It's not okay but they probably either A) assume stationarity of the various variables i involved  B) checked A) without providing details. I don't know the details of the regression ( or the paper ) but note that it's unlikely that the authors are making the cointegration assumption because that would be a jump that's unheard of as far as I know.
mark leeds
CC BY-SA 4.0
2021-09-12T15:23:18.260Z
@Emmanuel. The assumed underlying dynamics are expressed in footnote 10, not sure if that's useful? https://www.frbsf.org/economic-research/files/3-16.pdf
EB3112
CC BY-SA 4.0
2021-09-12T16:57:26.250Z
Based on what Emmanuel pointed out, It looks like they are assuming a partial adjustment model for the interest rate which does assume stationarity of the interest rate. I don't have time to read the rest of it but maybe other footnotes imply assumptions about the other variables. For details on partial adjustment models, see Harvey's text "Econometric Analysis of Time Series".
mark leeds
CC BY-SA 4.0
2021-09-13T13:22:45.713Z
Thanks mark and EB3112. I think original taylor rule is about long run relationship, yeah? If you read original paper and the plot in there, the relationship btween the taylor rule and FFR that taylor tries to capture is a longrun relationship, it seems. Or lemme say the author of the paper i sent wants to estimate the coefficients capturing this longrun relationship between interest rate, inflation gap and output gap, but if cointegration does not hold in the data as he say and he didn't check, it is proper to use OLS? He neither claim stationarity or non stationarity, but use OLS.
Emmanuel Ameyaw
CC BY-SA 4.0
2021-09-14T15:35:04.247Z
Hi Emmanuel: I'd have to read the whole paper in order to have the hope of making a useful comment. There are more than two variables which makes things more complicated. Note though that the use of an ecm does not imply the existence ( or assumption ) of cointegration. Cointegration implies an ecm formulation but ecm does not imply cointegration. Let me see if I can find a link to the paper that discusses this.
mark leeds
CC BY-SA 4.0
2021-09-14T15:43:07.137Z
Emmanuel: It won't answer the specific question you have but take a look at the paper: "Not just for cointegration: error correction models with stationary data", by Keele and De Boef. It's on the net but I can't figure out a way to link to it. It's a good paper for understanding that cointegration is not required for an ecm formulation.
mark leeds
CC BY-SA 4.0
2021-09-15T16:18:23.947Z
@ Mark. Many thanks for the comment and the paper. I will surely read it. But the data the author used is not also stationary, is it? The last time I applied ADF test to the federal funds rate, it didn't pass the test...although many still use federal funds rate with no transformation including bernanke's FVAR model. There are other taylor rule estimation papers I checked...but same thing. They neither check whether the variables are cointegtated or stationary but they apply ols anyway. Applying OLS doesn't require cointegration or stationarity? Kindly lemme know if my thinking is wrong here.
Emmanuel Ameyaw
<econometrics>
No claim whether data is stationary or non-stationary, but OLS is still applied?
Emmanuel Ameyaw
# No claim whether data is stationary or non-stationary, but OLS is still applied?

(Asked by: username_0 on 2021-09-11)

I am reading this famous paper 'Taylor’s Rule and the Fed: 1970–1997', and there is no check for stationarity, non-stationarity, integration or cointegration of the data, but the author just use OLS. When is that OK? I realized other studies estimating Taylor rule also do not transform the data in any way. Is it because interest rate, inflation, output gap appears stationary? The federal funds rate in levels fails ADF test when I checked, but it seems it does not matter much for Taylor rule estimation. Is that correct? When is violating stationarity or cointegration assumption ok?

**Tags:** econometrics
> **Comments:**
> **username_1**: Hi: It's not okay but they probably either A) assume stationarity of the various variables i involved  B) checked A) without providing details. I don't know the details of the regression ( or the paper ) but note that it's unlikely that the authors are making the cointegration assumption because that would be a jump that's unheard of as far as I know.  
> **username_2**: @Emmanuel. The assumed underlying dynamics are expressed in footnote 10, not sure if that's useful? https://www.frbsf.org/economic-research/files/3-16.pdf  
> **username_1**: Based on what Emmanuel pointed out, It looks like they are assuming a partial adjustment model for the interest rate which does assume stationarity of the interest rate. I don't have time to read the rest of it but maybe other footnotes imply assumptions about the other variables. For details on partial adjustment models, see Harvey's text "Econometric Analysis of Time Series".  
> **username_0**: Thanks mark and EB3112. I think original taylor rule is about long run relationship, yeah? If you read original paper and the plot in there, the relationship btween the taylor rule and FFR that taylor tries to capture is a longrun relationship, it seems. Or lemme say the author of the paper i sent wants to estimate the coefficients capturing this longrun relationship between interest rate, inflation gap and output gap, but if cointegration does not hold in the data as he say and he didn't check, it is proper to use OLS? He neither claim stationarity or non stationarity, but use OLS.  
> **username_1**: Hi Emmanuel: I'd have to read the whole paper in order to have the hope of making a useful comment. There are more than two variables which makes things more complicated. Note though that the use of an ecm does not imply the existence ( or assumption ) of cointegration. Cointegration implies an ecm formulation but ecm does not imply cointegration. Let me see if I can find a link to the paper that discusses this.  
> **username_1**: Emmanuel: It won't answer the specific question you have but take a look at the paper: "Not just for cointegration: error correction models with stationary data", by Keele and De Boef. It's on the net but I can't figure out a way to link to it. It's a good paper for understanding that cointegration is not required for an ecm formulation.  
> **username_0**: @ Mark. Many thanks for the comment and the paper. I will surely read it. But the data the author used is not also stationary, is it? The last time I applied ADF test to the federal funds rate, it didn't pass the test...although many still use federal funds rate with no transformation including bernanke's FVAR model. There are other taylor rule estimation papers I checked...but same thing. They neither check whether the variables are cointegtated or stationary but they apply ols anyway. Applying OLS doesn't require cointegration or stationarity? Kindly lemme know if my thinking is wrong here.  

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## 0 answers

