A simple test of simple rules against actual policy in the actual economy

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.]

Comments

[Brian Albrecht]

I know the original Taylor Rule is supposed to set the interest rate to hit a target inflation goal.

However, that always seemed like a secondary goal when I've heard it discussed. The benefit of such a rule is not simply that the central bank can better hit 2% inflation, but that everyone outside of the bank knows exactly what the bank will do. This removes policy uncertainty.

Obviously, if you think the big uncertainty is about inflation and not interest rates, the argument falls apart. I'm not saying it is convincing, but that seems to me the part that is stressed about "simple rules."

[Gregor Bush]

With the caveat that I used the current measure of the output gap instead of teh real-time measure, which is likely quite problematic, I get a coefficent of zero on the interest rate gap term for the full (1993-2014 sample). It's slightly negative in the post- Rowe/Tulk sample (2004-2014), as you might suspect, but still not statistically significant. So this would seem to confirm your orginal result but someone needs to do this properly with the real-time BoC output gap.

FYI, I did this test by including the "inflation gap" term in a simple error correction model of inflation.

[Nick Rowe]

Brian: fair point. But if it does no better at hitting the inflation target, it is a strange sort of "uncertainty" that gets reduced by the Bank's following a Taylor rule. People will know exactly what the nominal rate will be, *conditional on inflation and unemployment*, but they won't be any more certain about inflation and unemployment. Maybe, just maybe, one could construct a model where uncertainty about the deviations of actual policy from the Taylor Rule mattered more than uncertainty about each of the three components.

Gregor: fantastic! That was quick! (It would take me weeks banging my head against the keyboard in frustration trying to get the data onto a spreadsheet!)

Given your estimated coefficient of zero, it is not problematic at all that you used ex post rather than real time estimates of the output gap. You stacked the deck in favour of the Taylor rule, by implicitly assuming the Bank had final estimates of the output gap, *and it still came up with a zero coefficient*! (Unless you believe that ex post estimates of the output gap were somehow worse than real time estimates, which is extremely implausible.) That means that, even if the Bank had had a crystal ball that told it ex post estimates of the output gap, and could have constructed a Taylor Rule advice accordingly, it should have thrown away that extra advice. It told it nothing useful it didn't already know.

"FYI, I did this test by including the "inflation gap" term in a simple error correction model of inflation."

You lost me a bit there.

[Andrew_M_Garland]

What are the costs of inflation caused by the central bank? I don't see the estimate anywhere.

This is like discussing the good effects of bank robbery. The robbers spend more in the town and observers note the good effects on commerce. More people are employed. If the robbery can be kept small enough, then the depositors won't care (right?) and the town seems to benefit. A win-win.

The duscussion goes beyond printing merely 2% more each year to fund more government, but into how much can be printed to result in only a 2% effect on prices. Maybe government can spend 4% or 5% more each year in funny-money while creating a 2% increae in overall prices. That is even better for government, for as long as it works out. Price inflation of 4-5% might be noticed by the peasants, and would be excessive.

This is Keynesian scheme to collect more real resources through "rational" inflation. Amazingly, Keynes' commented on the matter.

( http://cafehayek.com/2009/06/keynes-on-inflation.html )
=== ===
[Keyned, edited] By a continuing process of inflation, governments can confiscate, secretly and unobserved, an important part of the wealth of their citizens. By this method, they not only confiscate, but they confiscate arbitrarily; and, while the process impoverishes many, it actually enriches some.

The sight of this arbitrary rearrangement of riches strikes not only at security, but at confidence in the equity of the existing distribution of wealth. Those to whom the system brings windfalls become 'profiteers', who are the object of the hatred of the bourgeoisie, whom the inflation has impoverished not less than the proletariat.

As the inflation proceeds, all permanent relations between debtors and creditors, the ultimate foundation of capitalism, become so utterly disordered as to be almost meaningless.
=== ===

( http://www.mises.org/daily/6752/How-Inflation-Picks-Your-Pocket )
How Inflation Picks Your Pocket
=== ===
[edited] The house-seller benefited because the new money reached him early, before the prices of the things he buys are bid up. For late-receivers of the new money, the prices of the things they sell are bid up (like wages for their labor) only after the prices of the things they buy (like groceries) are bid up even higher. So inflation (now alternatively defined as a general increase in prices) is a redistribution of wealth from late-receivers, who are taxed to support early-receivers.

Of course the government itself is among the earliest receivers, so it is one of the chief beneficiaries of inflation.
=== ===

[Nick Rowe]

Andrew: this post is not about whether 2% is the best target for inflation.

[Gregor Bush]

Thanks Nick. that makes sense.

""FYI, I did this test by including the "inflation gap" term in a simple error correction model of inflation."

You lost me a bit there."

So my original equation has a dependant variable that is the change in the BoC core inflation rate and has and last quarter’s level of inflation relative to target as an explanatory variable. The coefficient on that is negative and significant as you might expect given the anchoring of inflation expectations. I then added the interest rate gap term to the equation to see if it provided any additional information but it was not significant.

Perhaps that isn’t the right test and I shouldn’t have included the inflation gap term in the test equation (becasue it's already in the interest rate gap term). But he same result holds if you don’t bother with the lagged inflation gap term and just run a regression on the change in inflation with with only the interest rate gap as an explanatory variable. The interest rate gap variable dosen't appear to be significant in either case.

Note that I’m using Taylor’s rule and not an estimated rule.

[Nick Rowe]

Gregor: thanks. I get it now. The regression I would run is (for quarterly data:

inflation gap(t) = (no constant term) + B.interest rate gap(t-8) + MA(7) error term

(though the MA error term isn't really important). And the inflation rate is the year-over-year inflation rate, so it is (P(t)-P(t-4))/P(t-4).

The basic intuition is that *nothing* (that was available information at the time) should predict 2-year ahead deviations of inflation from the 2% target. Where "nothing" includes the interest rate gap between the Taylor Rule and actual policy

[Jason]

Nick,

You might find this interesting ... a prediction that Canada will start to undershoot its inflation target over the next couple years (or have to ramp up monetary expansion):

http://informationtransfereconomics.blogspot.com/2014/07/worthwhile-canadian-prediction.html

[Gregor Bush]

OK. I can do that. One issue though is that the mean of the dependant variable is not zero, it's -0.23 (core inflation has averaged 1.77% over the past 20 years not 2%). So the R2 of that equation is negative if there is no constant term. This is much less of an issue in the Rowe/Tulk sample becasue the mean of the inflation gap was only 0.1% from 1993 to 2003. But from 2004 to 2014, the mean of the inflation gap was -0.36.

In any event, if I go ahead and run it anyway, I get the result that the interest rate gap is negative but insignifcant for the full sample but negative and signifcant for the 2004-2014 sample - indicating that in the post Rowe/Tulk period the BoC has, if anything, placed too much weight on Taylor's rule.

[Nick Rowe]

Gregor: neat!

The core vs total CPI question is a bit tricky. The Bank uses core as its "operational guide", but if core is trending lower than total (which has been the case recently I think) it tries to keep total trending at 2% and lets core trend below 2%. So maybe leaving out the constant term (which is correct if you know that it is targeting 2%) biases things a bit if you have the core gap from 2% on the left hand side.

[Tom Brown]

Jason, that's awesome... how should I put this... Ustedes tienes cojones mas grandes... My Spanish isn't so great, but hopefully you get the picture. I don't often see a prediction like that on a sane econ blog (i.e. I'm excluding those run by media-whore charlatans trying to get you to buy overpriced gold or to stoke primal fears at the ballot box). I guess it helps that it's not your main line of work. (BTW, Vincent Cate is predicting hyperinflation in Japan in 1.5 years... (early 2016), so you're in fine company :D).

[Avon Barksdale]

Nick,

Your post is distressing in the extreme. I find it alarming that economists still adhere to discretion over rules 37 years after Kydland and Prescott. It is more than just annoying, it is economic snake oil that tricks the public into believing that economists can actually engineer society top down. This is simply the capture process at work with an economist going from having an idea to a policy proposal in the span of about 15 minutes - no Hayekian humility whatsoever. I know it looks like fun to try out all the models du jour on society, but these are people's live, not toy agents on foolscap. No one is smart enough to use discretion on an economy. I know economists think they are pretty smart, but as Deirdre McCloskey so eloquently put it in her 1990 book on the narrative of economic expertise, “If you're so smart why ain't you rich?” Sooner or later we will find ourselves truly understanding JFK's lament, “How could I have been so foolish to have trusted the experts.”

First, the Lucas critique and Kydland and Prescott tell us something deep. Furthermore, to the extent that we can avoid the original Kydland and Prescott criticism, we can use dynamic programing in the usual recursive sense and hence we are right back to a rule. Second, once we stop using rules, central bank independence is lost. Every single rent seeker and politician will argue for one monetary policy change over another and no institution's independence can survive that.

I am tired of seeing the let's-listen-to-wise-men arguments. It was “wise” men who cause the Great Depression through their discretion and that example more than any other should stand out as to what happens when we don't follow rules.

[Nick Rowe]

Avon: "Your post is distressing in the extreme."

My God, but you must have had a really sheltered reading experience!

See the bit about instrument rules vs target rules? That bit is of crucial relevance to Kydland-Prescott style arguments. Someone who uses his discretion to implement a target rule, and who is held accountable for hitting that target rule, is very different from someone who simply exercises his discretion. Plus, running empirical tests like the one I talk about here are part of that accountability check. If instrument discretion can implement a target rule better than an instrument rule, then which is more rule-like?

What caused the recession in Canada was not the Bank of Canada using its discretion; it was the Bank of Canada implementing the wrong rule. It should have targeted NGDP, not inflation.

[Tom Brown]

Does Prescott know much about monetary economics? Wasn't he the guy that said this?

"It is an established scientific fact that monetary policy has had virtually no effect on output and employment in the U.S. since the formation of the Fed."

I'd be surprised if Nick is enamored of his ideas about monetary economics (assuming that's the same guy).

[Nick Rowe]

Tom: Kydland and Prescott on rules vs discretion was a great paper IMO.

[Tom Brown]

Nick, thanks. Good to know. (When I read the above quote, I thought that must have made the MMists blow their tops, but I know that Sumner has said nice things about Prescott on occasion too: despite what Sadowski thinks)

[Avon Barksdale]

No, recessions are not caused by the Bank of Canada using the wrong rule. If economists are honest, we really don't know what causes recessions.

In the 1930s, the Fed turned a large but garden variety recession into a depression. What does "accountability" do for you when your discretion causes that?! Someone who uses his discretion to implement a target rule, and who is held accountable for hitting that target rule is nothing more than some grand active management scheme. Good luck with independence.

A human decision maker is not god. Whatever the discretion is, it is formulated on past information (the sigma algebra leading up to today). That means there is a rule, there is a dynamic program, that the decision maker is following. Make it public. I cannot tell you how tired I am of economists telling the public that they can engineer society if you just give them the power - that they can read the tea leaves better than the Oracle of Delphi. It's nonsense, it's dangerous, and it's anti-intellectual. What is even more shocking is that anyone can have an opinion about this who isn't an expert on dynamic programming and recursive methods. You don't see this in physics - when someone has an opinion on string compactification on manifolds of G2 holonomy, they tend to know something about differential geometry.

[Lorenzo from Oz]

Avon Barksdale: Australia has not had a technical recession (two quarters of shrinking GDP) since 1992. So I think we have some idea about what causes recessions -- demand shocks or uncompensated-for supply shocks or both. A question of "plucking".
http://employees.oxy.edu/mcintyre/Econ361-Spr07/Friedman-Plucking-Model.pdf

[Jerry Brown]

Avon Barksdale- you do understand that both society and the economy are created by people and are shaped by people, hopefully to serve us people, whereas the physical world studied in physics is not?

[Christiaan Hofman]

The only reason people like John Taylor keep saying that simple rules are better is because he has tested them against simple models (they may be pretty complex models, but they're extremely simple relative to the real economy.) That simple rules behave best in simple models should not be a surprise, but it is also completely meaningless. The real economy is much too complicated for simple rules, there are too many variables, and most of all, we simply don't understand macro well enough to device a sufficiently good simple rule. That's why discretion is always needed. I do hope this bill will never make it anywhere near a vote.

[Nick Rowe]

Avon: "A human decision maker is not god. Whatever the discretion is, it is formulated on past information (the sigma algebra leading up to today). That means there is a rule, there is a dynamic program, that the decision maker is following. Make it public."

Can you tell me how you drive your car? Sometimes it is much more useful to tell people that you are driving to Winnipeg, rather than the feedback rule for the movements of the steering wheel you will make to get there. Especially if there are unknown unknowns, like a bridge being down on the trans-Canada, which required a 600km detour, after chatting with locals and getting their advice. And what my test is showing is that human drivers can still outperform any currently-proposed mechanism for self-driving cars. Which is not to say that human drivers should ignore the advice given by such mechanisms; but they should not follow that advice 100%.

[Nick Rowe]

Christiaan: for any given model, there nearly always exists some rule that will do better than a given simple rule. The Taylor Rule, for example, is almost never optimal. But since we don't know what the true model is, and so we don't know what the optimal rule is, that is not a very telling critique of simple rules. The advocates of simple rules argue that they are robust, and will give a reasonably good (though imperfect) performance in any reasonable model. And the Bank of Canada tested that claim, by getting a variety of different models off the shelf, taking a handful of simple rules off the shelf, and seeing how each rule performed in a variety of different models. The results were mixed. My test here is an alternative way of testing simple rules, against actual policy (which won't be optimal either) in the actual world (for which we do not know the true model).

I look at my whole approach here as a very crude way of slowly improving feedback rules. We look at the actual policy, try to model the implied feedback rule that was actually being followed, then look for any systematic mistakes being made by that actual policy, then modify the actual rule in a direction that should reduce the magnitude of those mistakes. Because nobody designed the system, and we don't know what the optimal rule is, we can only learn from our past mistakes. But the system itself is changing over time, and there are always new things that happen, so perfection is unattainable, even in the limit. This ain't physics.

But we don't have much alternative to learning-by-doing. "Doing nothing" is not an option. There are 1001 different ways of doing nothing.

[wh10]

Nick - off topic. I took your advice 'to shut up and read a macro textbook.' So I've been doing it very carefully, but have still run into a roadblock as to how the loanable funds model can explain the mechanism by which the real rate adjusts to bring desired S and I into equilibrium. Is there an email or forum I could send you my thoughts and question? I've perused the couple posts you've done on this, but I don't think any of them get at what's bothering me. Thank you!

[Nick Rowe]

wh10: kudos to you!

Simplest answer: because that's where the Bank of Canada has to set the interest rate, otherwise inflation will either rise above (if I > S) or fall below (if S > I) target.

Nick dot Rowe at Carleton dot ca. But no promises.

[wh10]

Nick, I just sent you an email. Thanks so much! I feel like I could post here with a better chance of response given how diligent you are to getting back to everyone, but I don't want to derail the discussion.

[Gregor Bush]

Thanks Nick,

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 traget and stayed there for an extended period.

[Britmouse]

Isn't there a question about lags here? Do you think the BoC cannot influence the inflation rate (or output gap, or whatever) on a shorter horizon than that 2 year target? If so, "target 2% on the two year horizon" is merely an incomplete target rule, within which shorter-run stabilisation policy is discretionary?

e.g. looking at the BoC MPRs, why did the BoC set policy in early 2009 such that they expected undershoot the 2% for all of 2009 and 2010 despite a negative output gap? Was there no easier policy possible that had better short-run stabilisation, still satisfying the "2% by 2011" constraint?

It seems unsatisfying if "stuff happens for while, then the CPI rate hits 2%!" is all we can hold CBs to account for, even under IT, when the "stuff" they forecast can vary so wildly.

[Nick Rowe]

Gregor: well done and thanks! I have updated the post to tell people to read your comments, and have included your latest comment in the post.

Now, where's an American, Brit, Aussie, Kiwi, or Swede, who can do what Gregor just did? (Americans should probably leave the constant term in, because who knows what inflation rate the Fed was implicitly targeting?)

Britmouse: Yep. The targeting horizon has always been the fuzzy part in this approach. The Bank of Canada usually says something like: "we aim to bring the inflation rate gradually back to the 2% target over an 18 month to 2 year horizon". I think that their underlying fear is that trying to bring it back more quickly might require greater volatility in exchange rate and real GDP. You might even say that over that 2 year horizon they are implicitly targeting NGDP.

If it tries to target inflation at too short a horizon, when there are lags, you might even get a version of "instrument instability", with explosive oscillations in some variables.

What I sometimes do is repeat my tests for different horizons to see if it makes much difference. At short horizons the Bank generally fails my tests, which makes sense. It is not doing everything it can to bring inflation back to target next quarter (thank God). But once you are about 2 years out it didn't seem to make much difference.

[SvN]

Nick and Gregor
It's killing me that you're not using real-time output gaps.
The real-time gaps that Cayen and I constructed are available my code and data page (http://svannorden.org/code-and-data/), where you should also be able to find the code that generates them.

Does no one think that output gaps get revised anymore? We've seen very large revisions in the US since 2008. I don't know about Canada, though....

[Nick Rowe]

Simon: I had to check our old paper. We said: "Our measure of the output gap is (almost)8 a real-time measure; it is the same as was measured by the Bank’s QPM."

Footnote 8 says:
"Since estimates of the historical output gap are continually revised, a real-time output gap is
constructed using projections back to 1993Q3. The output gap prior to this date is taken as is from the
September 1993 projection. Sample cross correlations between the historical estimates available in
June 2003 and the aforementioned real-time output gap show a correlation of 0.922 over the entire
sample. Figure 5 shows a graphical comparison of the real-time output gap and the historical estimates
available in June 2003. Since each projection is run at the end of each quarter, our real-time measure of
the output gap is lagged one quarter. Other specifications of the output gap do not significantly change
our results."

Yep. If we (or Gregor) found a positive significant correlation, then we would really have to check to see if it held up with real time output gap data. But if it's not positive, I don't think it matters. Because the Taylor Rule wouldn't do better *even if* it used final revised data.

[Avon Barksdale]

"Can you tell me how you drive your car? "

First Nick, a computer can drive a car. It can fly a plane around the world, takeoff and land perfectly. The difference from monetary policy is that the Lucas critique does not apply to airfoils. It's sad to see you say: Doing nothing is not an option. Yes it is, an in many circumstances it is the best thing to do. Read Dixit and Pindyck. "Doing nothing is not an option" means that all I care about is power and I need to exercise it lest someone takes it away.

Look Nick, this discretion stuff is terrible. We learned long ago that the king's discretion on legal matters was a bad idea and we moved to a court based system strongly rooted in precedent. In many cases it would just be more expedient to move to summary execution of the clearly guilty without a trail, but we don't. Rules over discretion has made the law much better.

I don't believe for a moment that the central bank can drive the economic car. They are just not smart enough. DSGE are great for conditional modelling, but they are terrible unconditionally. (If you think otherwise, try running a hedge fund on some DSGE specification, see how far that gets you.) More often than not, the central bank will eventually put you in the ditch. It's disheartening to see economists advance the importance of central control, top down micromanagement of the economy. I still don't understand why some economists are deluded enough to think that they are some kind of social engineer, they are not. The Soviet's couldn't even get the price of coffee right, but you think that the magic discretionary powers of a team of central bankers can get interest rates just right? Shall we sit on pins and needles waiting for Superman (or Mark Carney or whoever)? You still haven't addressed the rent seeking incentive, the loss of bank independence, or the cult of personality that discretion brings. Stick to a public rule that is easy enough for everyone to anticipate. And then leave it alone - it is better to be roughly right than exactly wrong (and we will get exactly wrong with discretion eventually almost surely). I know that a rule will limit economists from trying out their pet theories and foil their attempt to show us how smart they are, but they can join a hedge fund for that, and just leave the rest of us to get on without them. I am sure we'll be fine.

As Sowell said, it takes considerable knowledge just to realize the extent of your own ignorance.

[Majromax]

@Jason:

Is your second graph really showing an inflation target? The super-exponential increase of the red line (since it's curved on a log/linear graph) suggests that the curve is really showing a price-level target, showing the ever-increasing monetary needs to compensate for past undershoots.

Regardless, I don't think simple extrapolation here is terribly informative. You're not really saying much about the actual economy, just that the Bank of Canada has been under-shooting its inflation target over the recent medium term. Regardless of the underlying model, if the Bank of Canada keeps under-shooting its target, it will get progressively further away from 2% price level increase.

[Nick Rowe]

Avon: "Stick to a public rule that is easy enough for everyone to anticipate."

We do not have discretion. We have a public rule that is easy enough for everyone to anticipate: set inflation at 2%. We are talking about how best to follow that rule.

Yes, computers can drive a car. And what my tests show is that the human driver can follow the announced rule of 2% inflation better than any currently proposed computer.

(And it's not strictly a 0-100 binary choice; the humans at the Bank of Canada are aided by computer models and simple rules like the Taylor Rule. It's a question of what the weights are.)

Does "doing nothing" with monetary policy mean: doing nothing to the price of gold, the nominal rate of interest, the target rate of inflation, NGDP growth, the price of peanuts, the money base, M1? or what?

Soviet central planners controlled relative prices by law, regardless of markets. A central bank that produces money cannot but decide how much money to produce, and it's decision will affect the nominal market price level. That central bank is one of the players in that market.

[Nick Rowe]

Plus: you are missing the whole point of Kydland and Prescott. The Bank of Canada has made a *commitment* to the 2% inflation rule. But if it wrote down an instrument rule to hit that 2% inflation target rule, it would need to keep saying several times a year: "Sorry, but we need to change our instrument rule again, because the updates on the econometric estimates show that our old instrument rule wasn't quite right, and we need to modify it a little if we going to keep to our 2% inflation commitment."

That instrument rule is not a rule at all, in the commitment sense. The 2% inflation rule is a rule. Changing it is a big deal.

[Majromax]

@Avon:

> We learned long ago that the king's discretion on legal matters was a bad idea and we moved to a court based system strongly rooted in precedent.

Actually, the Canadian system retains extremely wide discretion on legal matters. That ranges from the simple power to set laws (a matter for Parliament), granting of mercy (part of the Royal Prerogative), down to wide discretion for judicial sentences in criminal matters and prosecutorial discretion on when to lay charges in the first place.

Legal discretion is widely hailed as flexibility within the Canadian context, where Crown actions can vary with the circumstances to achieve a committed, principled outcome that balances the rule of law with mercy, rehabilitation, and recompense.

In that regard, legal discretion is broadly equivalent to the Bank of Canada's flexibility, whereby many different detailed actions are decided -- on a case by case basis -- towards the goal of achieving a fixed, committed, and democratically-given target.

[SvN]

Nick:
Mea culpa! I misinterpreted your description (above) of what you had done. The quote from your paper sounds like Good Practice.

Now if only we can persuade Gregor to run more regressions for us.......

[Gregor Bush]

Simon, I can't access dropbox. Do you have an updated real-time output gap calculated? Is it possible to post the series in Nick’s comment section? Btw, are you calculating it yourself or did you go back and pull the vintage BoC estimates?

Nick, the Sweden case would be interesting. My guess is that in recent years they've erred even more egregiously in the direction of Taylor’s rule. And, because the Riksbank publishes projections of their own policy rate (as well as other macro variables), it seems to me that there is a second test we could do. We could see whether the projected future interest rate gap explains future inflation. Perhaps the reason that inflation in Sweden has been 0% over the past 18 months instead of 2% is that it has been systematically communicating a reaction function that places too much weight on Taylor’s rule.
I think the UK is only DM where the interest rate gap MIGHT have a positive sign in recent years.

[Min]

Nick Rowe: "But if it does no better at hitting the inflation target, it is a strange sort of "uncertainty" that gets reduced by the Bank's following a Taylor rule. People will know exactly what the nominal rate will be, *conditional on inflation and unemployment*, but they won't be any more certain about inflation and unemployment."

The uncertainty is uncertainty about the central bank. The central bank needs to inspire confidence. One way to do that is to be clear and transparent about what you are doing. Greenspan may be a counter-example, but he relied upon his reputation as The Maestro, which is now tarnished. It is also important also to deviate from a clear rule upon occasion. Otherwise people lose confidence in your expertise. ;)

[Majromax]

@Min:

> The uncertainty is uncertainty about the central bank

Isn't that a second-order effect? If the markets at large think that the central bank can credibly meet its target (whatever it happens to be), then uncertainty as to just how it meets that target only matters in the detail.

Or to put it another way, isn't the point of a Taylor Rule the idea that we can replace central bankers with Folgers' Decaf Crystals who follow the prescribed formula and get largely the same results?

[Nick Rowe]

Gregor: You're on a roll! Interesting idea about Sweden!

"I think the UK is only DM where the interest rate gap MIGHT have a positive sign in recent years."

What is "DM"?

[Tom Brown]

@Majormax: re: Jason's plot. Check the equations at to bottom of Jason's post. That price level model results from his theory. Then take a look at this plot:

http://informationtransfereconomics.blogspot.com/2014/07/why-printing-more-money-could-have-done.html

Do you see the dashed black curve amongst all the colored ones? That's for a representative economy. When the kappa parameter from his model (see the equations I mentioned above) gets closer to 1, then the curves start flattening out and maybe even start decreasing slightly (as you go from right to left). Kappa is slowly varying for an economy, and *I think* economies tend to migrate from left to right over the years... i.e. the theory predicts that they slowly go from a QTM region to a region where P is less and less sensitive to changes in M.

So I think his model is showing that Canada is starting to transition out of the QTM region, and thus to stay on target with inflation they will need to grow M at geometrically ever increasing rates.

I let him know you commented, so he can straighten that out, but hopefully that's close enough for an interim answer.

[Tom Brown]

Should say "(as you go from left to right)"

[Nick Rowe]

Tom: please discuss Jason's post on Jason's blog. It's off-topic here.

[Tom Brown]

Will do, sorry.

[Jason]

@Majromax

Regarding your first point, Canada has been on a 2% average inflation trend since the 1990s:

http://worthwhile.typepad.com/worthwhile_canadian_initi/2013/01/the-bank-of-canadas-success-and-failure.html

The super-exponential curve is what is required to maintain that trend. It is neither undershooting nor overshooting the trend, so it can't be compensating for past undershoots (the red curve has no past undershoots -- it achieves 2% inflation exactly starting from "today"). Since the red curve is neither undershooting nor overshooting that trend there is no difference between a price level and an inflation target. If used e.g. a random walk then there would be a difference between a price level and an inflation target because the random walk would have undershoots and overshoots which the price level target would account for and the inflation target would ignore.

Regarding your second point: I'm not extrapolating the price level. I'm using the model at the bottom of the page. I am extrapolating the model inputs: NGDP and currency base. The model predicts that Canada will continue to undershoot the inflation rate (also undershooting the counterfactual 2% increase in the price level) by more and more in the future if it continues to print currency at a constant rate and RGDP increases at a roughly constant rate.

[Nick Rowe]

Jason: you too please.

[Min]

Moi: "The uncertainty is uncertainty about the central bank"

Majromax: "Isn't that a second-order effect? If the markets at large think that the central bank can credibly meet its target (whatever it happens to be), then uncertainty as to just how it meets that target only matters in the detail."

Look at the consternation over QE. There are now those who think that the Fed cannot increase inflation to the 2-3% range, and those who think that it is sowing the seeds for hyperinflation. Remember questions about whether the Fed could be "responsibly irresponsible"? Confidence does not only depend upon results. It can be maintained if people perceive you doing what they believe is the right thing, even if the results don't always work out. And, as Avon Barkley points out, people don't believe that bankers, or anybody else, are gods. Once you get mysterious, you are asking for a higher level of faith.

Majromax: "Or to put it another way, isn't the point of a Taylor Rule the idea that we can replace central bankers with Folgers' Decaf Crystals who follow the prescribed formula and get largely the same results?"

That is so for certain people, like Milton Friedman. Which is why you have to deviate from the clear rule from time to time. :)

Gigerenzer -- sorry, I don't remember where --, tells about a medical protocol that did better than physicians for initial diagnoses. The protocol was developed for non-physicians to refer patients to the right doctors. Doctors who learned the protocol then performed better than the protocol. They made use of the protocol, but also relied upon their medical knowledge to know when to deviate from it or overrule it. :)

[Nick Rowe]

Min: "They made use of the protocol, but also relied upon their medical knowledge to know when to deviate from it or overrule it."

That is my view about simple rules in a nutshell.

[Andrew_M_Garland]

Nick Rowe [edited]:
=== ===
(1) My whole approach here is a very crude way of slowly improving feedback rules. We look at the actual policy, try to model the implied feedback rule, look for any systematic mistakes, then modify the actual rule to reduce the magnitude of those mistakes.

(2) The system itself is changing over time, and there are always new things that happen, so perfection is unattainable, even in the limit. This ain't physics.

(3) We don't have much alternative to learning-by-doing. "Doing nothing" is not an option. There are 1001 different ways of doing nothing.
=== ===

Mr Rowe, your statement (2) is correctly the problem. The system (a few 100,000's of economic actors) changes over time with some new and surprising things ocurring. These participants determine the market for money, debt, and productive development.

In (1) you propose a very crude way of attempting to do some good. But, your only method is to guess about some forcible alteration of the system, try to measure what happened (over some years time), mostly guess again, and repeat. Meanwhile, the system is reacting to what you are doing and is evolving in some unanticipated way.

Why do you believe that your policy changes will ever ocurr in prompt time to reliably and positively affect the system? How do you know you aren't changing things for the worse? What evidence do you have that there is any policy which converges, given that there is no reliable limit to converge to?

If your approach could possibly work, then why not first do something simpler and much more profitable, such as predict the price of stocks? You are trying to do for the debt markets what I doubt you would try to do for the stock market.

In (3) you excuse your mistakes in advance by asserting that you have no choice, you must "do something", even if you must learn what to do along the way. The system you want to control has a few 100,000's of intelligent people assessing the situation. Why can you do better with your hand on some powerful switch, forcing them to do something different?

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.

[Nick Rowe]

Andrew: "Instead of controlling the money supply monopoly, why not advocate for competition in producing money."

There is no law against people using Bitcoin, or whatever, in Canada, AFAIK. Meanwhile, we work with what exists.

How do I know it converges? How do I know markets converge? They too are hunting for profit opportunities by spotting past mistakes in much the same way as I am. Plus, someone with a lot more computers than me tried it out in a slew of computer economies, and told me it did, though I could never figure out the details myself.

You got a better plan, while waiting for Bitcoin?

[Min]

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.

[Avon Barksdale]

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.

[SvN]

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."

[SvN]

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?

[Majromax]

@Andrew:

> In (1) you propose a very crude way of attempting to do some good. But, your only method is to guess about some forcible alteration of the system, try to measure what happened (over some years time), mostly guess again, and repeat. Meanwhile, the system is reacting to what you are doing and is evolving in some unanticipated way.

Isn't this the very essence of a control system? Using an approximate model for the system (here the economy and the various economic theories), apply a forcing (central bank action) that the model suggests will do some good.

Even though by necessity the model is imperfect, if its imperfections are bounded (not necessarily small, just not growing) then it can still be useful. I don't need to know the position of my coffee cup with microscopic precision in order to drink.

> Why do you believe that your policy changes will ever ocurr in prompt time to reliably and positively affect the system? How do you know you aren't changing things for the worse? What evidence do you have that there is any policy which converges, given that there is no reliable limit to converge to?

Is this the nihilist model of the economy?

It also seems belied by actual history. Canada's central bank is explicitly targeting 2% inflation over the medium term. This trend was not well-observed historically, prior to the target. Since adopting the target, inflation has closely tracked the 2% target.

Parsimony suggests that the central bank is indeed doing something right, and that its models have a functional correlation with the economy. Otherwise, we have to assume that the central bank is wrong but some other associated factor caused inflation to closely track the central bank's target over the recent period.

Occam's Razor suggests that conventional economics is the better explanation.

> If your approach could possibly work, then why not first do something simpler and much more profitable, such as predict the price of stocks? You are trying to do for the debt markets what I doubt you would try to do for the stock market.

I'm not sure that anyone would consider predicting stock prices to be easier than predicting broad economic trends. 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."

[Min]

@ Avon Barksdale

My apologies for getting your name wrong a few notes back. :(

[Nick Rowe]

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.

[Avon Barksdale]

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.

[Avon Barksdale]

"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.

[Jerry Brown]

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.

[Min]

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.

[Brian Romanchuk]

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.

[Min]

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.

;)

[Brian Romanchuk]

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!

;-)

[Nick Rowe]

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.

[Min]

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?