Friday, May 13, 2011

Fixing What’s Wrong with the Taylor Rule

I see four problems with the original Taylor rule:

  1. It’s not really a rule at all. The Taylor rule depends on an estimate of potential output. In practice, most of the discretion that goes into central banking is in the estimate of potential output. Even “discretionary” central bank policy is effectively constrained by the consensus of what would be considered reasonable policy actions, and any of those actions can be rationalized by changing your assumption about potential output. Usually, a central bank that has committed to following a “strict” Taylor rule has roughly the same set of options available as one that is ostensibly operating entirely on its own discretion.

  2. It doesn’t self-correct for missed inflation rates. Since the inflation rate in the Taylor rule is over the previous four quarters, the rule “forgets” any inflation that happened more than four quarters ago. This is a problem for four reasons:

    • It leaves the price level indeterminate in the long run, thus interfering with long-term nominal contracting and decisions that involve prices in the distant future.

    • It leaves the central bank without an effective tool to reverse deflation when the expected deflation rate exceeds the natural interest rate.

    • It reduces the credibility of central bank attempts to bring down high inflation rates, because the bank always promises to forgive itself when it fails.

    • It aggravates the “convexity” problem described below, because the central bank effectively ignores small deviations from its inflation target, even when they accumulate.

  3. It doesn’t allow for convexity in the short-run Philips curve. If the estimate of potential output is too low, for example, and the coefficient on output is sufficiently low, then, if the short-run Philips curve is convex, the central bank will allow output to persist below potential output for a long time before “realizing” that it has made an error. In the extreme case, where the short-run Phillips curve is L-shaped, the central bank may allow actual output to be permanently lower than potential output. More generally, the convexity problem can be aggravated by hysteresis effects, in which lower actual output leads to lower potential output, so that the central bank’s wrong estimate of potential output becomes a (permanently) self-fulfilling prophecy.

  4. It can prescribe a negative interest rate target, which is impossible to implement. This appears to have been the case for at least part of 2009 and 2010, although there is disagreement about the details.

So how do we fix these problems? I suggest the following solutions:

  1. Adopt a fixed method for estimating potential output. (One might allow future changes to the method, but they should be implemented only with a long lag: otherwise, they’ll interfere with the central bank’s credibility, since they can be used to rationalize discretionary policy changes.) Since I like simplicity, I suggest the following method: take the level of actual output in the 4th quarter of 2007 (when most estimates have the US near its potential) and increase it at an annual rate of 3% (the approximate historical growth rate of output) in perpetuity.

  2. Replace the target inflation term with a target price level term. In other words, express it as a deviation from a target price level that rises over time by the target inflation rate. To be clear what I mean by the “target inflation term,” take Taylor’s original equation
    r = p + .5y + .5(p - 2) + 2 (where p refers to the inflation rate)
    and note that I am referring to the “p – 2” term but not to the initial “p” term, which is not really a target but part of the definition of the instrument (an approximation of the real interest rate). In my new formulation, “p – 2” becomes “P – P*,” where “P is (100 times the log of) the actual price level and P* is (100 times the log of) the target price level (i.e., what the price level would be if the inflation rate had always been on target since the base period).

  3. Increase the coefficient on output. If you wish, in order to avoid a loss in credibility, you can also increase the coefficient on the price term by the same amount. What we have then is a more aggressive Taylor rule. It doesn’t solve the convexity problem completely, but it does assure that, when output is far from target, the central bank will take aggressive action to bring it back (unless the price level is far from target in the other direction). That way at least you don’t end up with a long, unnecessary period of severe economic weakness. (John Taylor claims that, according to David Papell’s research, there is “no reason to use a higher coefficient, and…the lower coefficient works better.” But that research only looks at changing the coefficient on the output term without either changing the coefficient on the inflation term or replacing it with a price term, as I suggest above. Having a too-small coefficient on the output term, as in the original rule, is only a second-best way of achieving the results that those other changes would achieve.)

  4. “Borrow” basis points from the future when there are no more basis points available today. In other words, if the prescribed interest rate is below zero, the central bank promises to undershoot the prescribed interest rate once it rises above zero again, such that the number of basis-point-years of undershoot exactly cancel the number of basis-point-years of (unavoidable) overshoot. This method will only work, of course, if the market knows what rule the central bank is following, hence (among other reasons) the need for a rule that really is a rule. If the rule is well-defined, the overshoot will be well-defined, the market will expect the central bank to “pay back” the “borrowed” basis points, and the central bank will be obliged to do so in order to maintain its subsequent credibility.

OK, let’s look at the big picture. What have I proposed? I have proposed nominal GDP targeting (along with a specific method for how to implement it). When the price level term and the output term have the same coefficient and both are specified as a deviation from target, the Taylor rule can be simplified by combining the price level target with the output target. Combining Taylor’s original 2% inflation target (re-expressed as a price level path target as per my suggestion) with my suggested method for estimating potential output, we arrive at a 5% nominal output growth path as the target.

If you wish, you can go further by making the rule forward-looking (using a forecast of nominal GDP instead of a lagged observation) and increasing the coefficient to a very high number. And you can enforce the credibility of the forecast by requiring the central bank to use the forecast implicit in a publicly traded nominal GDP futures contract, so that the market is putting its money where the central bank’s mouth is. You end up with the proposal that Scott Sumner has already made. People seem to think that Scott Sumner’s ideas about monetary policy are far out of the mainstream. But I’m not proposing anything radical here, just trying to fix some problems with the very orthodox Taylor rule.

DISCLOSURE: Through my investment and management role in a Treasury directional pooled investment vehicle and through my role as Chief Economist at Atlantic Asset Management, which generally manages fixed income portfolios for its clients, I have direct or indirect interests in various fixed income instruments, which may be impacted by the issues discussed herein. The views expressed herein are entirely my own opinions and may not represent the views of Atlantic Asset Management. This article should not be construed as investment advice, and is not an offer to participate in any investment strategy or product.


paine said...

bang away dear boy
the thing as is is a looped holed farce
designed to hocus pocus
what is really really
all about
domestic nominal
wage change control

taylor and his holey of holey rules
needs a pranging big time

nothing makes me happier then
a wallyworlder like yourself
administering the paddle ho

Mark A. Sadowski said...

Excellent post.

But I liked the nominal GDP level version of the Taylor Rule you created in the comment section at Econbrowser even better:

And, ultimately, making several adjustments to the Taylor Rule is a little akin to trying to save the horse and buggy by adding pneumatic tires, GPS, satellite radio, and feeding the poor beast genetically modified alfalfa.

In my opinion nominal GDP level targeting with a NGDP futures market would be more to the point, and would get us beyond our current obsession with interest rates, which in turn causes us to believe in zombie myths like the liquidity trap.

Matt Rognlie said...

Excellent post---I agree with (almost) all of it.

I'm curious, though, about the discussion of a highly convex short-run Phillips curve. Is there much evidence for this being the case? The New Keynesian Phillips curve is usually presented in log-linearized form (and thus it literally can't be convex), but it's not clear to me that a second-order approximation would reveal some kind of substantial convexity.

The results that an optimal Taylor rule can be achieved with no weight on the output gap rely on what Blanchard and Gali memorably called divine coincidence: the absence of any nontrivial real imperfections in the New Keynesian model other than monopolistic competition and sticky prices. But to think about how the output gap should figure into the Taylor rule, we need to make a stab at what those real imperfections are, and how they interact with monetary policy.

In fact, it seems possible to me that the Taylor rule should include estimates of the impact of these imperfections (e.g. "binding credit constraints") rather than the output gap itself, which might be a very flawed proxy.

Andy Harless said...


The traditional Phillips curve, in inflation-unemployment space, must be convex, because otherwise it would pass through the y-axis and imply the possibility of negative unemployment rates. And from what I recall, if you plot Phillips curves from the 50’s and 60’s (when inflation expectations were presumably close to constant), they certainly look convex, even away from very low unemployment rates.

For practical purposes, the issue may not really be whether the SRPC is convex but whether the LRPC is convex. Although it’s vertical (and therefore linear) in standard models, the empirical LRPC probably becomes quite convex in the neighborhood of the x-axis, as suggested by the recent IMF study of persistent, large output gaps. The likely explanation is downward nominal wage rigidity. If one were willing to target a sufficiently high inflation rate, the shape of the LRPC in the neighborhood of the x-axis would be academic, but given the seemingly unshakable consensus is that the inflation rate should be near 2%, the shape of the SRPC in practice may be determined to an important degree by the shape of the LRPC.

If you look at the US today (or Japan over most of the past 20 years), you see an output gap that would be consistent with inflation realizations far below expectations if the SRPC were linear, but you see actual inflation realizations only slightly below expectations. It’s hard to continue believing in the Phillips curve at all unless you believe it has significant convexity (or if you believe that our output gap estimates are totally wrong, but in that case, the Phillips curve concept isn’t of much practical value).

Scott Sumner said...

You can defend my NGDP targeting proposal more effectively than I can--excellent post.

I agree that PCs are fairly convex, although oddly they plunged right through the x-axis back in the gold standard days. Obviously the shape of the PC is very dependent on all sorts of structural factors, as well as the nature of the monetary regime (a good example of the Lucas Critique.)

Anonymous said...

why assume GDP growth of 3% in perpetuity? clearly this changes over time - and indeed the estimates i've seen of US potential GDP growth range from about 2.2% to 2.85% (OECD, robert gordon, etc.)

Benjamin said...

I like this--but at zero bound do we go to QE?

sean said...

Hi Andy

I'm the Finance editor at Before It's News. Our site is a People Powered news platform with over 2,500,000 visits a month and growing fast.

We would be honored if we could republish your blogs rss feed in our Economy category. Our readers need to read what experts like you have to say.

Syndicating to Before It's News is a terrific way to spread the word and grow your audience. If you are interested in syndicating with us, please contact me at

sean [at] beforeitsnews [dot] com

Thank you

Flow5 said...

The Taylor rule doesn't measure anything. The formula uses yesterday's variables which have no future nexus. It’s useless.

Donald Pretari said...

"As it was, the collapse of nominal GDP drove the “fiscal multiplier” to zero, leaving us with more debt and nothing to show for it."

I'm a bit confused here. If the Debt were the problem, shouldn't our interest rates be going up as investors would want more return for their risk?

Andy Harless said...


Today's federal debt isn't a problem today (especially since the Fed can just buy it without causing any ill effects), but it could theoretically become a problem once the recovery takes place (assuming it ever does). If it weren't for political problems and the distortionary impact of taxation, this shouldn't matter: we would just raise taxes after the recovery, just in time to prevent the economy from overheating. As it is, the federal debt is a little bit worrisome (though not very much so in my own opinion). At some point in the future, the Fed may have to sell it back into the market (or else raise the interest rate on reserves, which amounts to the same thing, since reserves are essentially government debt issued by the Fed instead of the Treasury), and that could end up crowding out private capital formation and/or costing the government a lot for debt service.

I think that was David Levey's concern about "more debt," though I don't understand what he means when he says that "the collapse of nominal GDP drove the 'fiscal multiplier' to zero." You can believe that the fiscal multiplier is zero if you think the Fed fully offsets fiscal policy, but the collapse of nominal GDP seems to indicate just the opposite. If the Fed wouldn't offset the increased private sector demand for money that caused nominal GDP to collapse, then why would one expect it to offset fiscal policy?

Donald Pretari said...


Thanks for the explanation.


Patrick said...

Andy wrote: "The traditional Phillips curve, in inflation-unemployment space, must be convex, because otherwise it would pass through the y-axis and imply the possibility of negative unemployment rates."

1. Theoretically: it could be anything, including concave, truncated at the value u=0.

2. Empirically: it's a mess, at times convex, at times concave, because it's just not a structural relationship.

Yasir Khalid said...

Interest on reserves is a convenience, because you can raise it without disrupting markets, but it doesn't allow the central bank to avoid losses that would otherwise be necessary. TV Schedule

London team building said...

I love it! I actually think that they should have gone for all cuts of meat, or meat related. We could have had Pork Chop, T-Bone, Meat Ball, Pepperoni, Ham Hocks, Jerky, Hausenpheffer and Riblet :) Plus Kevin, of course. Ha ha ha ha ha. Too much fun. I legitimately would have submitted Riblet and T-Bone, however. I totally want to name a family of otters now. London team building

recuperacao de hd said...

Thanks for the informative blog. The place else may possibly just I get that kind of info written in such a excellent approach? I’ve a venture that I’m just now operating on, and I’ve been on the glance out for such info.recuperacao de hd

Yasir Khalid said...

The root problem is the confusion between behavioral and identity relations. I examined this in my article "Low Savings or a High Trade Deficit", which appeared in Challenge, July/August 2007. office partitioning

living trust cost said...

is very exciting and informational. I am trying to decide on a career move and this has helped me with one aspect. Thank you so much!Your article is very exciting and informational.rust living trust cost

Yasir Khalid said...

I’m glad you enjoyed the interview (and got some validation on your own ideas!). cheap bitcoin hosting

surechlor salt cell said...

I realize it turned out my own option to learn to read, yet My partner and i actually considered you would have got something fascinating to state. Almost all My partner and i find out will be a variety of whimpering regarding something that one could deal with if you were not also chaotic searching for interest.For additional data click on surechlor salt cell

Yasir Khalid said...

I believe this is pretty close to where MMT'rs (or horizontalists, or whatever) like Winterspeak stand on the question of "what is money". reviews on the truth about cellulite

sedotan plastik said...

This is truly a unique blog. Literally, this blog is just out of this world.sedotan plastik I have never seen anything like this before. Wow! Just keep the quality of your to this extent.

Yasir Khalid said...

PPS: I’d love to hear your thoughts on this guide. After you share the guide on Twitter, Facebook and Google+, leave a comment below with your feedback. Smart Price Warehouse

Tanveer Ali said...

In these circumstances, the only viable choice left is to provide his or her home completely before this is foreclosure and marketed off to auction. Quick Home sale

Tanveer Ali said...
This comment has been removed by the author.
Tanveer Ali said...

Because of improve in the interest of individuals towards the on the internet casinos, the quantity of on the internet casinos is improving very quickly. official sites

Tanveer Ali said...

That might create audio sluggish, but culling excellent quotations from bigger performs is both an efficient way to become acquainted with a author's perform and an efficient way to create his or her ideas psychologically convenient. wise sayings

Yasir Khalid said...

My mother used beer (blonde beer) for her hair many years ago, and chocolate bubble bath is my favorite one. Thanks for the other great tips! Healthy Snack Recipes and Cooking Tips Agen Judi Bola, Taruhan Bola Terbaik dan Terpercaya said...

I always want and love reading quality contents. Keep sharing. Best wishes for your further efforts. Well done. Agen Judi Taruhan Bola, Casino Online Terbaik dan Terpercaya di Indonesia, IRpoker Indonesia Rupiah Poker online, poker Zynga Facebook, Agen Judi Domino Online Indonesia Terpercaya, OLB365.COM AGEN JUDI BOLA ONLINE, AGEN JUDI CASINO ONLINE INDONESIA TERPERCAYA

clearwater salt cell said...

You know your projects stand out of the herd. There is something special about them. It seems to me all of them are really brilliant clearwater salt cell


cukup inspiratif juga ya, kalau bermain Coba Agen Judi Bola sangat berbeda dengan ini, lebih sama dalam permainan irpoker indonesia yang juga memenangkan situs Agen Judi Taruhan Bola, Casino Online Terbaik dan Terpercaya di Indonesia, hanya OLB365.COM AGEN JUDI BOLA ONLINE

bodyarmor said...

The dissertation and thesis-writing services we provide give you the results you need, guaranteed.

bodyarmor said...

The dissertation and thesis-writing services we provide give you the results you need, guaranteed.bodyarmor

Gujjar rehman said...

Great web site you’ve got here.. It’s hard to find good quality writing like yours nowadays. I honestly appreciate people like you! Take care! camp Tenerife

caspa said...

Excellent site !! wonderful blog post.It is one of the most interest page in the net. I never expect that there are lots of contents that are useful to my assignment. Thank you so much guys caspa

steve7876 said...

I just painted the backs of my books shelves too: orange. I'm still working on finding good stuff to put on said bookshelves. your shelves look great, love all the white accents! custom website design orlando

Anonymous said...

e cigarette reviews, e cigarette reviews, electronic cigarette reviews, smokeless cigarettes, e cigarettes, e cig forum

GNC coupons said...

Yesterday sucked for me! Well most of the day. Luckily I had a few of my sites hosted here: GNC coupons

steve7876 said...

All the same, writing poetry is a difficult task! Need to work on myself and on my world view, as do modern authors! galapagosholidays

Marco Fisher said...

I was able to find the details that I was searching for. I must thank you for the initiatives you have made in writing this article. I am expecting the similar best efforts from you in the future as well. term paper

shahbaz said...

The vibrant colors of this plate screams EAT ME! haha.. I love the photos they are stunning... really!
I don't have a green thumb neither... no luck in growing my own garden... but I keep trying...maybe there's still a chance? halong bay

jenny said...

This is really great post, keep sharing this kind of posts which thing helpful to make big boobs

Clear Glass Ornaments said...

Well just decided to create a blog, which I have been wanting to do for a while. Thanks for this post, it’s really useful Clear Glass Ornaments

shahbaz said...

What could you possibly ever need help with! I get inspired by you! Tonight I'm going to try to make this. Looks so delicious, and healthy too! Watercolor real estate

Accredited GED Online said...

Really important written content. the information that you shown is hard to faith and many superbly i liked the way you afford things here.

agen poker said...

Jika Anda tertarik untuk membuat uang di taruhan online agen sbobet, berikut adalah beberapa tips untuk membantu Anda sumber link meminimalkan risiko dan menjadi sukses dalam hal ini ratu itu. Kunci untuk menjadi sukses dalam taruhan klik ini dan perjudian, apakah Anda melakukannya ratupoker secara online atau offline adalah untuk meminimalkan kerugian miyabipoker Anda.

poker online said...

Betting agen ibcbet telah menjadi cara yang menyenangkan dan menarik untuk menikmati olahraga agen ibcbet favorit Anda atau permainan tangkas online indonesia dan membuat uang ekstra agen bola tangkas ketika melakukannya. Bahkan, taruhan agen poker telah ada selama berabad-abad. Dengan munculnya internet, taruhan online poker online bahkan menjadi lebih populer karena juga telah menjadi dewa poker lebih nyaman. Secara teknis, taruhan online bola tangkas dapat benar-benar dianggap sebagai turunan dari perjudian agen bola terpercaya online. Namun, perkembangan bola tangkas telah mengalami telah berubah menjadi sebuah konsep taruhan casino sbobet yang sama sekali baru. Selain itu, telah menjadi jauh lebih sedikit sulit untuk menempatkan taruhan online, sehingga tidak perlu mengeluarkan banyak waktu dan usaha.

shahbaz said...

This article is very very encouraging to the Christian who is really willing to follow Christ at all costs. All people who consider themselves Christians should read this article! dolor de cabeza

ZealVouchers said...

This will enable significant broadband penetration at the rural and remotest areas and can be a boon in M2M adoption. ZealVouchers

shahbaz said...

If you were looking for someone to embody the essence of a boss lady, Jenna Lyons would be it. She's not only the president and executive creative a fashion label for prime quality Italian leather items.3CouponCode

shahbaz said...

First You got a great blog .I will be interested in more similar topics. i see you got really very useful topics , i will be always checking your blog thanks. Escape Room The Key

steve7876 said...

I also benefit from learning the assessments, but learn that alot of people ought to stay on essay to try and add worth in the direction of the authentic weblog release.Lithium polymer battery discussion

happy friendship said...

mothers day
mothers day 2015
happy mothers day
happy mothers day 2015
happy mothers day Quotes
happy mothers day Quotes from daughter
happy mothers day Quotes from son
happy mothers day Poems
happy mothers day Poems from daughter
happy mothers day Poems from son
happy mothers day Wishes
happy mothers day Wishes from daughter
happy mothers day Wishes from son
happy mothers day Messages
happy mothers day Messages from daughter
happy mothers day Messages from son
happy mothers day Greetings
happy mothers day Greetings from daughter
happy mothers day Greetings from son

Happy Mothers Day 2015
Happy Mothers Day
Mothers Day 2015
Happy Mothers Day 2015 Wishes
Happy Mothers Day 2015 Gifts
Happy Mothers Day 2015 SMS
Happy Mothers Day 2015 Card
Happy Mothers Day 2015 Poem
Happy Mothers Day 2015 Images
Happy Mothers Day 2015 Pics
Happy Mothers Day Wishes
Happy Mothers Day Gifts
Happy Mothers Day SMS
Happy Mothers Day Card
Happy Mothers Day Poem
Happy Mothers Day Images
Happy Mothers Day Pics

Li-ion battery said...

I read that Post and got it fine and informative. Li-ion battery

steve7876 said...

We tried your Red Pepper Sauce with Sour Ceam-Lime Drizzle on halibut and it was fantastic! My husband kept repeating "This is five star!" I must say I agree. Not only is it delicious, but it is so pretty and colorful! Initial public offering

easter bunny said...

happy easter poems
happy easter greetings
happy easter messages
happy easter songs
happy easter 2015
happy easter
happy easter wishes
Easter Wishes 2015
Easter SMS
Happy Easter Images
Happy Easter Day
Happy Easter Quotes

happy easter messages
happy easter poems
happy easter greetings
happy easter songs
easter quotes
happy easter quotes
funny easter quotes
happy easter 2015
happy easter
happy easter wishes
Easter Wishes
happy easter images

obat herbal said...

obat ambeien atau wasir racikan herbal penyakit wasir obat wasir racikan herbal pusat herbal denature obat wasir tradisional obat herbal wasir obat tradisional untuk mengobati cara mengobati penyakit ambeien atau said...

Saya sangat senang dengan artikel kamu, setelah lelah kuliah kelas akuntansi dan menggarap makalah di web ini, sungguh jenuh dengan perhitungan dan teori ilmu ekonomi tersebut. ingin sekali setelah kuliah langsung berlibur ke kepulauan karimunjawa, kata posting ini sih bagus dan banyak spot foto yang bisa dikunjungi, oh ya sekedar info juga nih, kalau mau beli mesin fotocopy yang murah entah itu merk epson atau xerox, bisa kunjungi kami sebab kami adalah toko online yang sudah lama menjual barang berkualitas dan dipercaya, misalkan saja jam tangan keren wanita yang sudah banyak laku di jakarta dan indonesia, saya juga web tersebut disini agar yang ingin tampil cantik dengan jam tangan murah bisa terwujud. sedangkan bagi anak anda yang gemar dengan anime seperti one piece episode baru dengan subtitle indonesia dapat di download disini dengan format file rata – rata adalah 3gp sehingga mudah dimainkan di ponsel, sebab saat ini kan banyak sekali ponsel yang memiliki aplikasi bagus untuk memainkan video, bukan hanya video untuk selfie saja sudah menggunakan kamera ponsel, apalagi sekarang ada cara untuk memperindah fokus kamera hp di artikel ini, pasti semua ingin hpnya menjadi canggih. tapi ingat gan, kalau main hp juga perlu memperhatikan kesehatan mata loh, kalau mau membaca cara agar kamu tetap sehat dan terhindar berbagai penyakit gula darah, simak disini saja karena sudah saya jelaskan tentang berbagai tentang cara pencegahan diabetes.

steve7876 said...

Positive site, where did u come up with the information on this posting?I have read a few of the articles on your website now, and I really like your style. Thanks a million and please keep up the effective work.ceramic body armor

Sumit Thakur said...

I have made a huge collection of Happy Mothers Day Images and pictures...Go and get them for free.
Happy Mothers Day 2015
Happy Mothers Day Images
Happy Mothers Day Pictures

Sumit Thakur said...

I have made a huge collection of Happy Mothers Day Images and pictures...Go and get them for free.
Happy Mothers Day 2015
Happy Mothers Day Images
Happy Mothers Day Pictures said...

Its a great pleasure reading your post.Its full of information I am looking for and I love to post a comment that "The content of your post is awesome" Great work