# Talk:Taylor rule

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## Plagiarism?

This page is copied almost word-for-word from the Federal Reserve Bank of San Francisco's website, here. I'm not sure if this is with permission. —Preceding unsigned comment added by 193.190.134.66 (talkcontribs)

This was taken almost verbatim from San Fran Fed Reserve Page. —Preceding unsigned comment added by 207.243.125.101 (talkcontribs)

I'm not sure when these comments were written, but they are no longer true. Rinconsoleao (talk) 14:33, 24 September 2010 (UTC)
The page history indicates that those comments were written in May 2007. I subsequently reformatted this section and added the signatures and title, but did not change the content. They would have been referring to this old version of the article. JRSpriggs (talk) 18:27, 24 September 2010 (UTC)

## Missing Coefficients

The coefficients a are not defined, nor is there discussion as to how they are chosen in practice.PhysPhD 19:30, 14 September 2007 (UTC)

Agreed. This is still a problem a month later. Crasshopper 01:02, 18 October 2007 (UTC)

According to Nelson (2000), "UK monetary policy 1972-97: A Guide using Taylor rules", Taylor (1993) asserted that a coefficients of a(pi)=1.5 and a(y)=.5 adequately modeled US Federal Reserve policy up to that time. There is nothing magical about those particular values though, and Taylor (1999) seems to favor higher values. In general though, a(pi) should be greater than one if the economy is to achieve its inflation target on average. (Measure for Measure 19 Oct 2007)

## Value of a sub pi

Taylor's original paper wrote the rule like this (see his original paper, page 202):

${\displaystyle i_{t}=\pi _{t}+r_{t}^{*}+a_{\pi }(\pi _{t}-\pi _{t}^{*})+a_{y}(y_{t}-{\bar {y}}_{t})}$

(In the original paper, r was used in place of i, and p in place of ${\displaystyle \pi }$, but the equation was of the form shown here.)

However, many papers today write the rule like this:

${\displaystyle i_{t}=R_{t}^{*}+A_{\pi }(\pi _{t}-\pi _{t}^{*})+A_{y}(y_{t}-{\bar {y}}_{t})}$

Notice that these two versions of the rule are exactly logically and mathematically equivalent. But setting ${\displaystyle a_{\pi }=0.5}$ in the first version of the rule is equivalent to setting ${\displaystyle A_{\pi }=1.5}$ in the second version of the rule.

Therefore there has been some confusion among editors as to whether the correct value of the inflation coefficient is 0.5 or 1.5. The answer just depends on how we write the rule. Currently the rule is written in its original version (after all, the page cites the original paper). Therefore the correct value is ${\displaystyle a_{\pi }=0.5}$. But alternatively we could write the rule the second way, which might be more familiar to students today, and then the correct value would be ${\displaystyle A_{\pi }=1.5}$.--Rinconsoleao (talk) 15:31, 6 August 2008 (UTC)

Your argument is only partially correct...anyway the 1,5 are from this paper http://www.bankofengland.co.uk/publications/workingpapers/wp120.pdf —Preceding unsigned comment added by 137.208.80.253 (talk) 03:31, 15 April 2010 (UTC)

## Units needed

I assume that the nominal and equilibrium real interest rates are given in %/year; and that the actual and desired rates of inflation are also in %/year. So ${\displaystyle a_{\pi }\,}$ can be dimensionless as 0.5 is. However, the logarithms of the actual and potential output must be dimensionless. This means that we need some units (presumably %/year) attached to ${\displaystyle a_{y}\,.}$ However, the suggested value of 0.5 does not have any such units. JRSpriggs (talk) 18:14, 10 April 2009 (UTC)

## What is the optimal rate of inflation?

Milton Friedman showed that the ideal value for the (risk-free short-term) nominal interest rate is zero. If we assume that at some time ideal conditions exist, the Taylor rule

${\displaystyle i_{t}=\pi _{t}+r_{t}^{*}+a_{\pi }(\pi _{t}-\pi _{t}^{*})+a_{y}(y_{t}-{\bar {y}}_{t})\,}$

becomes

${\displaystyle 0=\pi _{t}^{*}+r_{t}^{*}+a_{\pi }(\pi _{t}^{*}-\pi _{t}^{*})+a_{y}({\bar {y}}_{t}-{\bar {y}}_{t})\,}$

and thus

${\displaystyle \pi _{t}^{*}=-r_{t}^{*}\,}$

which is true not only under ideal conditions, but under any conditions. In words, the optimal rate of inflation is the negative (i.e. actually deflation) of the equilibrium real (risk-free short-term) rate of interest. JRSpriggs (talk) 18:14, 10 April 2009 (UTC)

Apparently, John B. Taylor himself uses ${\displaystyle r_{t}^{*}=+2.0\%/\operatorname {year} \,}$ for the ideal real interest rate, ${\displaystyle a_{\pi }=+0.5\,,}$ ${\displaystyle \pi _{t}^{*}=+2.0\%/\operatorname {year} \,}$ for the desired rate of inflation, and ${\displaystyle a_{y}=+50\%/\operatorname {year} \,}$ (where 50% = 0.5·100%, assuming the logarithm in y is the natural logarithm). So he simplifies the rule to the form
${\displaystyle i_{t}=1.5\pi _{t}+(50\%/\operatorname {year} )(y_{t}-{\bar {y}}_{t})+1.0\%/\operatorname {year} \,.}$
If one changes the desired rate of inflation to ${\displaystyle \pi _{t}^{*}=-2.0\%/\operatorname {year} \,}$ (notice the change of sign) as I indicated above, then this becomes
${\displaystyle i_{t}=1.5\pi _{t}+(50\%/\operatorname {year} )(y_{t}-{\bar {y}}_{t})+3.0\%/\operatorname {year} \,.}$
In other words, I would suggest increasing the constant term in the rule by two percent per year. JRSpriggs (talk) 20:28, 17 April 2009 (UTC)

## Timing

The edits by 94.161.36.128 (talk · contribs) which I reverted a month ago made me wonder whether we should replace ${\displaystyle i_{t}\,}$ with ${\displaystyle i_{t+1}\,}$ in the Taylor rule

${\displaystyle i_{t}=\pi _{t}+r_{t}^{*}+a_{\pi }(\pi _{t}-\pi _{t}^{*})+a_{y}(y_{t}-{\bar {y}}_{t})\,}$

giving

${\displaystyle i_{t+1}=\pi _{t}+r_{t}^{*}+a_{\pi }(\pi _{t}-\pi _{t}^{*})+a_{y}(y_{t}-{\bar {y}}_{t})\,.}$

Although we would like the policy makers' responses to be instantaneous, that is unrealistic. They need to measure the inflation rate and economic output before they can use that information to set an interest rate target. What do you think? JRSpriggs (talk) 23:39, 4 July 2010 (UTC)

## The New Palgrave Dictionary of Economics reference

So pp. 2000-2004 are page numbers? If they are, sorry, my mistake. --Biblbroks (talk) 08:46, 9 August 2010 (UTC)

Well, I am not sure that they are because I do not have the book. But according to the website, it has over 7000 pages. So they certainly could be page numbers. Thus we must give the editor who added that information the benefit of the doubt. JRSpriggs (talk) 06:31, 10 August 2010 (UTC)

## Picture

The picture was deleted on the basis that it does not contribute to our understanding of the Taylor rule. — Preceding unsigned comment added by 130.39.171.137 (talk) 16:15, 12 October 2011 (UTC)

I put it back. Illustrations make articles more friendly and attractive. JRSpriggs (talk) 17:46, 12 October 2011 (UTC)

The picture was deleted again as the article is not about making it friendly or attractive. Moreover, this article is not a biography. For the article to remain as scientific as possible, we need to add a picture that helps explain the Taylor rule. — Preceding unsigned comment added by 130.39.171.137 (talk) 16:08, 27 October 2011 (UTC)

If you can make such an informative picture or find one which is public domain, then please add it. Until then, I will put back the picture of Taylor. JRSpriggs (talk) 04:38, 28 October 2011 (UTC)
That would appear to be the case. If you google search for images of the taylor rule lots show up, a graph would be a great addition. And probably more helpful then the goofy picture of taylor.MilkStraw532 (talk) 23:54, 28 October 2011 (UTC)
The picture of Taylor is inappropriate to this wiki article. The pic of John B. Taylor is appropriate in his biography http://en.wikipedia.org/wiki/John_B._Taylor — Preceding unsigned comment added by 64.134.144.155 (talk) 00:32, 16 November 2011 (UTC)
To the IP-vandal: Please stop vandalizing this article: taking out a picture; adding a name which is not used for this rule; deleting the economics template; and insulting me. JRSpriggs (talk) 11:37, 16 November 2011 (UTC)

Dr. Hayo has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

I would mention in one of the first sentences that it is a specific form of an interest rate rule, in contrast to, say, a money growth rule. .

I would not phrase the rule so much in terms of employment, e.g. 'It is intended to foster price stability and full employment' or 'when output is above its full-employment level'. As long as the rule is specified in terms of an output gap, there is no one-to-one relationship with full employment.

I would mention that the parameter used in Tyalor rules can either be based on a rule of thumb argument, like in Tayor's original paper, or by using econometric estimates.

An estimate of the ECBs Taylor rule in a comparative perspective is presented in ' Hayo, B. and B.Hofmann (2006), Comparing Monetary Policy Reaction Functions: ECB versus Bundesbank, Empirical Economics 31, 645–662.'

Finally, I would mention that a Taylor rule can be approached in terms of a 'positive' research question, how does the Fed's Federal Funds rate react to inflation and output, or a 'normative' research question, namely is the Fed's interest rate setting in line with the recommendations of a Taylor rule?

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Hayo has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference : Bernd Hayo & Britta Niehof, 2013. "Studying International Spillovers in a New Keynesian Continuous Time Framework with Financial Markets," MAGKS Papers on Economics 201342, Philipps-Universitat Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).

ExpertIdeasBot (talk) 18:50, 27 June 2016 (UTC)