A "simple rule" is a formula that tells a central bank how to set the nominal interest rate as a fixed function of a small number of variables. The Taylor Rule, which sets the nominal rate as a function of the gap between actual and target inflation, and the gap between actual and potential output, is the classic example of a simple rule. Are simple rules better than discretion? Here's how we can do a test to find out, and the results of an old test where simple rules failed to do better than actual policy.
We need to distinguish between "instrument rules" and "target rules". The Bank of Canada, for example, sets a nominal interest rate instrument to target 2% inflation. The Bank of Canada follows a very simple target rule: "set (future) inflation at 2%". But it does not follow any instrument rule like the Taylor Rule. Instead it uses its discretion. It looks at everything it thinks might be relevant, and adjusts the nominal interest rate instrument accordingly to ensure that, in its own judgement, future inflation will converge to the 2% inflation target. "Simple rules" (in this context) means "instrument rules". If the Bank of Canada kept the 2% inflation target, but used a Taylor Rule instead of discretion to try to hit that same 2% inflation target, it would be following a simple rule.
Simon Wren-Lewis and Tony Yates have both recently posted about simple rules. They make good and sensible critiques. Tony tells us that John Taylor tells us that there is a bill before the US Congress that would require the Fed to follow a simple rule. So simple rules are topical.
Since simple rules are topical, I have an excuse to plug an old bit of empirical research I did with David Tulk. Plus, since that research is now a decade old, and could easily be updated (and could easily be replicated for other countries aside from Canada), I am hoping to entice someone to update it and replicate it. (I am too incompetent to do it by myself, and David has moved on to bigger and better things).
Our test was very simple. Take a simple rule off the shelf. The Taylor Rule for example. Then plug in the historical actual numbers for the inflation gap and the output gap into the formula (strictly, you need to have real-time estimates of the output gap to do this properly) to calculate the nominal interest rate specified by that simple rule. Then calculate the "interest rate gap" as the difference between the nominal interest rate specified by the simple rule and the actual interest rate set by the Bank of Canada. Then look at the correlation between that "interest rate gap" and the subsequent [update: we used a 2-year lag, because the Bank had a roughly 2-year targeting horizon] "inflation gap" (the gap between actual and target inflation). The sign of that correlation is telling you something important.
If you find a positive (and statistically significant) correlation between the interest rate gap and the future inflation gap, that is telling you the Bank of Canada should have put more weight on the "advice" given by the simple rule and less weight on its own judgement. (But it does not tell you it should have put 100% of the weight on the advice given by the simple rule and 0% weight on its own judgement.)
The intuition is also simple. If in one period the interest rate gap is positive, that means the simple rule is saying that the Bank of Canada was setting the nominal interest rate too low to keep future inflation at the 2% target, and so the simple rule is saying that future inflation will rise above the 2% target. And if in another period the interest rate gap is negative, that means the simple rule is saying that the Bank of Canada was setting the nominal interest rate too high to keep future inflation at the 2% target, and so the simple rule is saying that future inflation will fall below the 2% target. By looking at the sign of the correlation between the interest rate gap and the future inflation gap, we can test those implicit forecasts made by the simple rule.
To cut a long story short (read the paper for the details): simple rules did not perform well in our test.
The most plausible explanation is this: it is not that simple rules give bad advice; rather, the advice they give was already incorporated into the Bank of Canada's decisions, to which the Bank of Canada then added its own judgement from looking at other variables. The policy implication is not that the Bank of Canada should completely ignore the advice given by simple rules; the policy implication is that the Bank of Canada should put no more weight on that advice than it actually did. Simple rules leave stuff out, and what they leave out matters too.
This fits with what Simon and Tony are saying.
But maybe our test wasn't powerful enough, because we only had 10 years of data, because the Bank of Canada had only been targeting inflation for 10 years. 10 years later, with 20 years of data, the results might be different. Or might not. More research is needed (sorry).
(To keep it simple, I have written this post as if I were an orthodox New Keynesian/Neo-Wicksellian, which is what I was 10 years ago.)
[Update: please read Gregor Bush in comments below. Gregor has updated Rowe/Tulk for Canada. His main finding: "This probably isn't shocking but using overall inflation in the test equation instead of core results in a coefficent that is more negative and more significant on the interest rate gap. Taylor's rule, for example, wanted the overnight rate to be about 300bps higher than it actually was from late 2010 to early 2012 and of course inflation subsequently dropped well below target and stayed there for an extended period." What that result means is that the Bank of Canada should have put less weight on the Taylor Rule's advice than it actually did.]
Worthwhile Canadian Initiative 
Andrew_M_Garland: “Monopolies don’t do well achieving optimal production. Instead of controlling the money supply monopoly, why not advocate for competition in producing money. Competitive markets engage more capital and brains than monopolies, and are less affected by political manipulation.”
Mebbe so. But they have tendencies to act alike at the same time, leading to potentially runaway imbalances, to times of too much money and times of too little money, to booms and busts. We saw this pattern clearly in the US in the 19th century. We have also seen it return with deregulation over the past few decades.
Andrew,
I like you I have a bias for markets and a bias against government which has a monopoly on violence and uses it.
Having a government produced fiat money is not a bad idea if we bring in hard rules, eliminate the cult of personality, and remove all discretion. With these rules, money becomes standardized in much the same way as weight and measures. Transaction cost in society would be much higher if we had the Rona foot, the Canadian Tire yard, and the President’s Choice pound just as if we had the RBC lira, or the CIBC dollar. Standardization helps. But, to make this standardization work without the negative consequences of the government’s monopoly on violence, we must remove all discretion from central banks, eliminate active monetary management, and reduce the central bank to essentially a computer with a public rule system. There is no need for all the economists at the Bank of Canada writing recipes that call for just a touch more eye of newt or toe of frog. Your statement about the system changing was made formal by Robert Lucas, known today as the Lucas critique. You are absolutely right, if they’re so smart, why aren’t they rich from anticipating stock market?
And Nick,
While there is no law against bartering with assets, you can’t pay your taxes from the resulting trade with anything but dollars.
Gregor; You should be able to find the file now at http://svannorden.org/?attachment_id=153
This has a variety of real-time gaps calculated using the methods documented in Cayen and van Norden (2005) (i.e. mostly the same as Orphanides and van Norden.) I’ve not updated them, but code for producing the estimates is included, so that should be easy. (I’m happy to help if you have questions.)
These are not the gaps used by the good folks at the BoC. I’m not aware that they make those vintages public in an organized fashion (unlike, say, what the good people at the FRB Philadelphia do for FOMC estimates of output gap and the NAIRU.) I tried once to get them to publish them but a very senior, smart and short bank official felt that this would not be prudent.
BTW, if anyone knows of a Canadian source for original vintage Canadian data, please let me know. The Statistics Canada RTDAT page still claims that their data will be offline “…until the release of the historically revised data in October 2012. At that time, the RTDAT can be used to analyse the new estimates resulting from the historical revision.”
Andrew and Avon: “Instead of controlling the money supply monopoly, why not advocate for competition in producing money.”
Last time I looked, there were many different currencies in the world, many of them quite popular (although I think the CAD is still among the favourites.) And while governments can insist on being paid in their fiat money, that’s a pretty small fraction of all transactions. There’s no shortage of examples of people substituting towards “hard” currency when they have doubts about the local stuff. Over at EconBrowser, Menzie Chinn nentioned an IMF study noting that recent sanctions against Russia were having precisely such an effect.
Of course, if you think that competition in producing money is such a good thing….why did so many nations want to join the Eurozone? and why do they still have a line-up?
@Andrew:
@ Avon Barksdale
My apologies for getting your name wrong a few notes back. 😦
Majromax: that was a rather good answer. Better than mine.
One problem with the stock market analogy is that the Bank of Canada issues “stocks”, and thus, ultimately, controls the price of those stocks. A (small) individual buyer of stocks doesn’t have the same affect on the fundamental value of those stocks. Not sure if this matters.
SvN,
I did not suggest that we move to private money, only that we move to a solid rule system that removes discretion. Discretion leads to cults of personality. And then we get the rent seekers. Carney went on about corporate “dead” money, Poloz feels a higher price for the US dollar is good, at Jackson hole people ask, “Was Greenspan a great central banker or the greatest of all time?”, and so on, and on. When a personality becomes all encompassing, no one will hold him to account – don’t underestimate the bully pulpit. It’s nonsense and it leads to real problems. The price of independence is rules.
“The macroeconomy has the law of large numbers working for it, where individual variation is smoothed over an extremely large number of people and firms. The stock market is all about the microeconomy and predicting that same variation. It’s the difference between predicting the flight path of a single bird versus “geese fly south for the winter.”
Nick and Majromax,
OK, that is just nonsense and Nick as an economist you should know better. The stock market is about risk sharing across the entire economy – it’s not some micro effect thing. All assets are redundant to the Arrow security decomposition that they represent. Remember Nick, the stock market is really about cross insurance, risk sharing, and hedging the consumption paths across the whole economy. I don’t see how the stock market fails to be about the law of large numbers, as you put it.
And if you think that setting interest rates based on some broad trend is easier than calculating stock prices, try running a fixed income prop desk and you will see just how complicated “interest rates” really are. It’s actually much harder than equities. (As a quant, I can tell you that equity derivative pricing is a bit like quantum mechanics, fixed income is more like quantum field theory in its complexity.) We need simple central bank rules precisely because the problem is so complicated. You’re right Nick, this is not physics, it’s a lot, lot harder, so quit pretending you can fine tune with discretion.
Avon Barksdale has convinced me about the need for the rules. But I want to be the one to make the rules. Simple Rules. The 1st rule will be- No complaining about the rules. I am working on Rule #2. If you are an expert in dynamic programing and recursive methods, and have an opinion about string compactification on manifolds of G2 holonomy with a firm grasp of differential geometry, comments in the form of a short (politely worded please) letter will be welcomed to assist in formulating rule #2. All letters must demonstrate an understanding of the complexities of quantum field theory and of the redundancy of assets to the Arrow security decomposition that they represent. Letter writers that have run a fixed income prop desk, or any other business dealing with horse manure are especially invited. The rest of you- please remember Rule #1.
I think that if the stock market had the law of large numbers working for it, to take a ready example, Long Term Capital Management would still be chugging along. It has the law of large numbers working for it, until it doesn’t.
Avon Barksdale: “We need simple central bank rules precisely because the problem is so complicated. . . . You {cannot} fine tune with discretion.”
Excellent point.
The assumption that monetary policy must follow rules miases the elephant in the room – fiscal policy. If the government does not want to passively play along with the effect of monetary policy, there’s not a lot the central bank can do about it.
If you believe in DSGE models, that falls under the Fiscal Theory of the Price Level.
If you don’t, you probably end up with some variant of Post-Keynesian economics, where fiscal policy is typically assumed to be very important.
Brian Romanchuk: “If the government does not want to passively play along with the effect of monetary policy, there’s not a lot the central bank can do about it.”
Well, there are those who believe this:
If the central bank does not want to passively play along with the effect of fiscal policy, there’s not a lot the legislature can do about it.
😉
They’re free to believe that, but the legislature could always just announce a tax of 100% on interest income paid by the government, ending the economic effectivenes of the central bank. Fiscal wins again!
😉
Brian: central banks can issue 0% nominal interest currency that people nearly always (Zimbabwean exceptions aside) accept. Governments nearly always (ZLB exceptions aside) have to pay positive nominal interest rates to get people to accept their bonds. A 100% tax on interest income paid by government would constrain governments to run balanced budgets (or surpluses), but would not constrain central banks.
But this is totally off-topic for this post. End of discussion.
Brian Romanchuk: “the legislature could always just announce a tax of 100% on interest income paid by the government, ending the economic effectivenes of the central bank.”
Nick Rowe: “central banks can issue 0% nominal interest currency”
Sounds like we have a winner. Greenbacks, anyone?