Natural rate =/= trend or average

Start with the actual unemployment rate in (say) Canada over (say) the last 20 years (the years of targeting 2% inflation). Calculate the average unemployment rate over that 20 years. Call it "Ua".

Now imagine a policy counterfactual. Suppose that the Bank of Canada had done exactly what it did do, plus or minus a lot of random stupid things. But all those random stupid things had no effect on average inflation, or on trend inflation, over that same 20 years. Because they were mean zero random stupid things, and there were enough of them that their effects on inflation all cancelled out on average. Call the average unemployment rate in that counterfactual "Uc".

Would you expect Uc to equal Ua?

I wouldn't. I would expect Uc to be bigger than Ua. Doing random stupid things makes things like unemployment worse on average, for a given average inflation rate.

Or imagine a second policy counterfactual. Suppose the Bank of Canada had had a crystal ball. So it did a lot fewer things that seemed sensible at the time but look random and stupid from the benefit of 20/20 hindsight. Again, assume possession of the crystal ball has no effect on average inflation and on trend inflation. Call the average unemployment rate in that second counterfactual "Ub".

Would you expect Ub to equal Ua?

I wouldn't. I would expect Ub to be less than Ua. Not doing things that were random and stupid from 20/20 hindsight would make things like unemployment better on average, for a given average inflation rate.

Only in a linear model, where the actual unemployment and inflation are a linear function of deviations of monetary policy from trend, or deviations from optimal monetary policy, would Ua=Ub=Uc.

Even if you have a natural rate model, where the average monetary policy (the inflation target) has zero effect on unemployment, the average level of unemployment will depend on the variance of monetary policy around that average, and on the covariance of monetary policy with respect to other shocks hitting the economy. Unless the model is linear, and the short run Phillips Curves are not curves, but are straight lines.

That is one of the most important reasons why it matters to get monetary policy right. The booms and busts do not all cancel out on average. You can maybe define the natural rate independently of mean monetary policy. But you cannot define the natural rate independently of the variance and covariances of monetary policy. You cannot empirically estimate some policy-invariant natural rate simply by taking some sort of smoothed average trend of the actual rates. If you do that over a period when monetary policy made bigger than normal mistakes (from hindsight), like recently, and if I am right about the direction of non-linearity, you will overestimate the natural rate of unemployment.

Brad DeLong says (correctly, I think) that the New Keynesian research program included:

"3. Business cycle fluctuations in production are best analyzed from a starting point that sees them as fluctuations around the sustainable long-run trend (rather than as declines below some level of potential output)."

Funnily enough, both Old Keynesians, and Milton Friedman's "plucking model", see fluctuations more as declines below some level of potential output than as fluctuations around the sustainable long run trend. They are (mostly) fluctuations below the sustainable long run trend. The plucking model is very non-linear. Recessions can be as big as monetary policy is too tight. But there is a limit to how big booms can be, however loose monetary policy is. Recessions and booms don't average out. With an extreme version of the plucking model, where there are no booms at all, the average measures the average recession.

The data seem to support the plucking model. [Update: see Robert Waldmann's closely related post, which provides links to more evidence.] My eyeballs say it looks like that too. Unemployment meanders along, not doing much, then it suddenly jumps up, then slowly declines back towards its previous trend. The bigger the previous jump up, the bigger the eventual decline.

Even if there were no trend in inflation between now and before the recession, it is not correct to take the average unemployment rate over the last few years as an empirical estimate of the natural rate. Your sample reflects a period when the variances and covariances of monetary policy were worse than normal, and worse than we hope they will be in future.

Comments

[David Andolfatto]

"My eyeballs say it looks like that too. Unemployment meanders along, not doing much, then it suddenly jumps up, then slowly declines back towards its previous trend."

Nick, as it turns out, this "cyclical asymmetry" in unemployment rate fluctuations emerges as a natural phenomenon in models of labor market search. See, for example, http://www.jstor.org/discover/10.2307/136240?uid=3739744&uid=2&uid=4&uid=3739256&sid=21103216201803

[Nick Rowe]

David: neat! From the abstract, my guess is that the intuition works like this: with no macro shocks for a long time, there is only a small turnover from individual-specific shocks, and search unemployment is low. A negative macro shock breaks up the matches, and it takes a long time to rebuild them even if there are no more shocks. But a positive macro shock doesn't do much. It just makes existing matches even more profitable for both sides. Something like that? (I see Arnold Kling's PSST as a more complicated version, because you need to match lots of people together in a team, not just firm and worker.)

[Sanjay Mittal]

Also, doing “random stupid things” forces people to change jobs for no good reason. And the more job changing there is, all else equal, the higher will unemployment be.

[The Market Fiscalist]

"Doing random stupid things makes things like unemployment worse on average, for a given average inflation rate."
r
Wouldn't 50% of the these random things be random sensible acts reducing the unemployment rate ? So Uc would be the same as Ua but perhaps with a higher variation ?

[Nick Rowe]

Sanjay: good point.

TMF: Hmmm. I think that would only work if the initial monetary policy were totally silly.

I think if we assume that actual monetary policy = perfect plus silly noise, then adding even more silly noise makes it worse on average, even if the new silly noise is uncorrelated with the initial silly noise.

[David Andolfatto]

Nick,

Basically, yes. The intuition is simpler than that: It's easier to kick down a sandcastle than to build it back up. It's the same with relationships.

One also observes the asymmetry in the "heat wave effect" in mortality rates. A spell of bad weather increases the mortality rate on impact. A spell of good weather has no immediate effect on births (unless you have some weird theory of the undead suddenly coming back to life ;) )

[Nick Rowe]

David: beautiful!

Now, to my mind, most of the kicking down of sandcastles is due to monetary policy tightening + sticky prices. But building them back up again (assuming monetary policy lets you) is a mostly real phenomenon. And once they are all built back up again, a sudden loosening of monetary policy doesn't help you build (many) more.

Good monetary policy is just the absence of bad monetary policy that kicks down sandcastles.

[Min]

"Even if you have a natural rate model, where the average monetary policy (the inflation target) has zero effect on unemployment, the average level of unemployment will depend on the variance of monetary policy around that average, and on the covariance of monetary policy with respect to other shocks hitting the economy."

In that case, the "random stupid things" do not have to be stupid. Random is enough. :)

[Jon]

And the policy debate since the 1700s has been about constructing rules to accomplish this.

[J.V. Dubois]

As for variance it immediately reminded me of this old post of yours: http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/12/why-reality-is-skewed-and-so-newspapers-are-biased-towards-bad-news.html. It applies to majority of optimizing systems, I really enjoyed comment by Jeremy Fox.

[Nick Rowe]

JV: Good point. I hadn't seen that. That is why random shocks are mostly bad. Jeremy Fox's comment was the best.

Jon: who did you have in mind from the 1700's? David Hume?

[Mark A. Sadowski]

Nick,
Off Topic.

I just wanted to commend you for a series of excellent comments on IOR at Pragmatic Capitalism this weekend:

http://pragcap.com/stop-with-the-cutting-ioer-will-increase-lending-madness

I recommend that everyone read them, the comments alone are as worthy as a post in their own right.

[Andy Harless]

It has always been obvious that the Phillips curve was convex (and becomes even more obvious when you try to contemplate unemployment rates below zero), but New Keynesians like to linearize everything to make the math tractable. However, there was a line of research that started at the IMF (or was it at the Bank of Canada?) in the 1990's (associated with Doug Laxton and various co-authors, Clark, Rose, Meredith, etc.) that sought to draw out the implications of the Phillips' curve's actual convexity. One of the big implications is that the cost of policy mistakes is high, because the process of undoing mistakes is expensive. (This of course was back in the days when most economists thought of inflation as an unambiguously bad thing.) Also Laxton et. al. (I forget which "et al" in particular) argued that the "Natural Rate of Unemployment" should refer to a different concept as the "NAIRU," because one (I forget which was which) is the rate theoretically consistent with a stable inflation rate at any point in time, and the other is the unemployment rate that you actually need to have, on average, in order to avoid price instability. The latter is higher, because convexity, and the fact that you don't hit the target perfectly all the time, means that you need to let the unemployment rate get fairly high to offset the inflationary effects of the periods when it gets just a little bit too low.

Another aspect of convexity (which I don't know if Laxton et. al. dealt with) is that it gives you a lower signal-to-noise ratio when the unemployment rate is low. You don't know if inflation is behaving well because you're close to the NAIRU or if you're actually significantly above the NAIRU and have been hit with shocks that are disguising the disinflationary conditions (or conversely, if the inflation rate is falling, you don't know if it's because you're getting hit with shocks or because you're far above the NAIRU). I have argued that this strengthens the case for level targeting over growth rate targeting, and for having a larger real output component in the target (i.e. NGDP targeting over "flexible inflation targeting").

[Nick Rowe]

Mark: thanks! And I want to commend Cullen Roche for running a very friendly blog, where he and his other commenters tolerated my strong disagreements with what they were saying with good grace and humour.

Andy: Yep. I know Bank of Canada people have been making similar points for some time. Lipsey (not BoC, but definitely Canadian) has always insisted that the Phillips Curve is curved, and not a straight line. And Doug Laxton et al are all mostly University of Western Ontario mafia too. It seems to be a Canadian theme, for some reason!

Good point about signal/noise ratios.

[Majromax]

> I recommend that everyone read them, the comments alone are as worthy as a post in their own right.

I second the request for a post in its own right. I've commented here on the matter of interest on excess reserves, but I'm very much a layperson and would love to see Nick's consolidated take on it.

[Mark A. Sadowski]

Nick,
"And I want to commend Cullen Roche for running a very friendly blog, where he and his other commenters tolerated my strong disagreements with what they were saying with good grace and humour."

That's good to hear. I was blocked from commenting at his blog so obviously my experience is very different.

[Philippe]

I was also blocked from commenting at his blog. He censors people, like Mark, who disagree with him in a way he doesn't like, whilst pretending to be "open minded".

[J.V. Dubois]

Mark: Yeah, pretty good posts by Nick over there. However it just confirms to me that many poeople like to get themselves confused by the whole banking stuff. I wish all of them read Nicks post about banks being actually in the business renting houses instead of loan selling. I think it would clear out the things much more - no more talks about risks, assets, liabilities, debt, collateral and all that thrown in a sentence as if it somehow magically explains why IOR cannot be increased AND decreased at the same time AND why even current level of IOR is not good.

However I am almost sure that there would be at least one thing that could come up out of it - that people did not pay proper attention to basic economics. Like for instance what is supply and demand, what is quantity supplied, or quantity actually sold/purchased etc. It seems incredible to me that people casually throw these most basic concepts in a very confusing way.

[Odie]

J. V., As far as I remember Nick does not make the distinction in his post about banks looking for renters, not empty houses. However, an empty house is like a non-performing loan to the bank; a bad asset, an earnings-loss. That is the reason next to liquidity while banks don't just buy houses. They will only do that if they have a tenant who moves into it. Like a bank does not just make loans but lends money to willing borrowers. Banks want the rent payments; that is the only thing they are interested in. You can look at Islamic banking for reference. Even there banks don't just buy houses at random. That distinction is important because it shows that banks cannot just create money and spend it. They will want their money back (plus interest) so they lend it.

[Cullen Roche]

Phil & Mark,

I didn't block your comments. I just put them on moderate. Every once in a while commenters start acting very hostile towards other people and I just don't have the time to police every comment so I put people on moderate (or I rarely block them if they're obviously just a jerk). I must have warned Phil about this a dozen times with his incessant MMT rants. Holy crap it gets annoying hearing the same two or three MMT lectures over and over again....

Anyhow, if you leave comments that aren't hostile or combative then I take people off moderation. I am happy to publish comments by people who can contribute positively to the discussion, but I adhere to a pretty strict commenting policy. It keeps the comment section clean, friendly and productive.

Thanks for (maybe) understanding. And Nick, thanks for the forum and sorry for the distraction.

Cullen