Principal-agent problems and level-path targeting

Suppose you hire an agent to do a job. The agent's level of production p depends on the agent's effort m and on a mean-zero shock from nature s. So p = m + s. You observe p, but you do not observe m or s. Your agent observes s and p only after he has chosen m.

This is a standard principal-agent problem. If p is lower than you wanted, you cannot tell whether this is because your agent put in less effort than you wanted or because there was a negative shock.

But if you hire the same agent to do the same job year after year, and if the shock is serially uncorrelated between one year and the next, it gets a lot easier to solve the principal-agent problem. You tell the agent he has an annual production target p* for each year, and a cumulative target over T years of Tp*. He can miss the annual target, but if he misses the cumulative target by more than X% he will be fired. In the limit, as T goes to infinity, the average level of p must approach p*, for any finite X. And the agent knows that if he slacks off more this year he will have to work extra hard in future years to have the same probability of keeping the job.

This is probably one reason why people like to give repeated business to the same car mechanic.

Let p be the inflation rate, let s be the central bank's forecast error, and let m be the monetary policy instrument setting that will deliver p if s=0. Forecast errors should be mean-zero and serially uncorrelated if the central bank has rational expectations. Price level path targeting is like telling the central bank it will be fired if its cumulative misses of the inflation target p* add up to more than X%.

As Scott Sumner said a few months back (I can't find the link), level-path targeting keeps the central bank honest. It knows it will have to make up for past "mistakes" in future.

Comments

[Min]

"Price level path targeting is like telling the central bank it will be fired if its cumulative misses of the inflation target p* add up to more than X%."

Oh, that's a real threat, fer shure, fer shure.

What happened to the CB as Deus Ex Norris?

[Nick Rowe]

Min: this makes the CB as Chuck Norris even stronger. Everyone knows that if he doesn't do his job, he gets replaced by Bruce Lee.

[srin]

So, who gets fired? The entire Board or the Chairman? At some point is the institution itself dissolved to be replaced by another more competent institution? Should we have Congressional hearings to discuss these decisions or are there bright lines, so the decision is automatic? What would be considered mitigating circumstances?

[Majromax]

> So, who gets fired? The entire Board or the Chairman? At some point is the institution itself dissolved to be replaced by another more competent institution?

Isn't this a pointless exercise? If a nation's central bank isn't responding to its own legislatively-set targets, then the nation has larger problems than the particular form of the target.

What you're asking is the equivalent of "what if they started a central bank but nobody came?"

[Nick Rowe]

srin: without going too deeply into the Coyne Affair, I think the Minister of Finance would issue a written directive to the Governor of the Bank, who would either follow it or resign. Basically, the Department of Finance would take over. Not an outcome anyone would want, so it would be very unlikely ever to come to that.

[Mike Freimuth]

For the record, I don't think you will get the first best even in the principle agent problem even with a repeated interaction because there will still be an incentive to slack off for a few years and earn some rents before getting fired which means you will have to pay the agent more in order to make him fear being fired enough to put in the efficient (or something near the efficient) amount of effort. Sort of an efficiency wage story.

I don't think this has any implications for monetary policy, I just like talking about micro stuff. However, in wondering if it has any implications for monetary policy, one can't help but wonder what the objective function of monetary policy makers looks like. Do they benefit from "tighter" monetary policy in the short run? Do they fear being fired? If they want to hit the target every period in the first place, there isn't really a principle agent problem.

If instead, we have a potential incompetence problem: we're not sure whether inflation is low because of some random shock that will be made up for in the future or because monetary authorities are not actually following the optimal (or perhaps stated) policy target, then how long do we have to observe inflation below the stated target before we decide that it may be the latter? And what happens then?

[Nick Rowe]

Mike: Paragraph:

1. Agreed. long-term relationships reduce but do not eliminate the problem (unless the interest rate is 0% and time goes to infinity!).

2&3. It's always difficult taking these sorts of models too literally, when applied to things like central banks. But an announced price level path target does lead to greater transparency and accountability than an inflation target. Suppose a central bank aiming at 2% inflation will hit anywhere between 0% and 4% in any one year. Saying that they must resign if annual inflation is less than 0% or greater than 4% gives them enormous latitude. But saying that the price level must never deviate more than 2% from the target path gives them very little latitude. A random walk has an infinite variance, in the limit.

[anon]

Mike Freimuth, couldn't the agent post a bond equal to the expected rents, which she forfeits if she is fired? With the standard principal-agent problem this doesn't work all that well, due to the possibility of a negative shock. However, with Nick's strategy, we are essentially scaling the shock down by averaging over repeated realizations, so the amount of risk we have to care about is quite a bit smaller. So ISTM that the solution should shift that much closer to just paying the agent for results.

[Min]

Nick Rowe: "Everyone knows that if he doesn't do his job, he gets replaced by Bruce Lee."

;) ;) ;)

You know, I may have seen one of Bruce Lee's first movies. With some time to kill in Chinatown, I went to a kung-fu movie. Near the end there was a huge melee on a beach. Among the fighters I saw what looked like a 16 or 17 year old Bruce Lee. He took a punch and did a standing back flip with no discernible crouch or other preparation. Amazing! I stayed for the credits and I recognized the Chinese character for Li or Lee for the family name, but I could not read the given name.

[Nick Rowe]

anon: "....we are essentially scaling the shock down by averaging over repeated realizations, so the amount of risk we have to care about is quite a bit smaller."

Yes. That's the key. All the standard trade-offs between various bads in principal-agent problems remain, but by averaging over repeated realisations those bads get smaller. Like an inward shift of the PPF between bads.

Min: I can only vaguely remember one Bruce Lee movie. But I liked his acting, as well as his moves. Maybe I'm a bit low-brow.

[anon2]

Back to the whole monetary policy-fiscal policy interaction and who moves last debate, did you see this? http://macromarketmusings.blogspot.com/2014/12/what-do-john-cochrane-paul-krugman-and.html Do you agree with the conclusion that that monetary policy and fiscal policy can be complements?

[Andy Harless]

OK, I'm going to blow my own horn and claim that it was I, not Scott, who said that level targeting keeps the central bank honest. In the context, I was actually supporting the case (made by Vaidas Urba) against Scott's preferred method of enforcing a level target.

[Nick Rowe]

Andy: Yep. reviewing your old comment, I do see you making the point:

"Vaidas makes good points about futures targeting. I would have the same concerns, and as a result it's not clear to me that there is a net advantage to using the futures markets as opposed to merely targeting an internal forecast of NGDP (or preferably NNDI). Obviously the gross advantage is that it takes away the central bank's opportunity to engage in deception and self-deception by either semi-intentionally biasing the forecast or not trying very hard to hit it. But this strikes me as a relatively minor advantage, at least compared to the generic advantage NGDP level path targeting over flexible (or, even worse, strict) inflation targeting. Level targeting does a lot to keep the central bank honest, even if it's allowed to use its own forecast and not directly penalized for missing it."

[Nick Rowe]

anon2: I just found your comment in the spam filter. sorry about that.

I read David's post. I'm unsure about it. Money and bonds pay different rates of return, so you can't just add them together in that (M+B)/P = PV(S) equation. Plus, those rates of return will not be exogenous wrt the time-paths of M and B. Plus, money usually pays a negative (real) rate of return, so PV(S) is undefined, because you are discounting at a negative interest rate, so the terms do not converge to zero as time goes to infinity.

[JKH]

Nick,

OT -

An attempt to understand the Cochrane paper:

http://monetaryrealism.com/john-cochranes-monetary-policy-with-interest-on-reserves/

[Jacques René Giguère]

anon: "putting a bond forfeited if she is fired" Essentially the british army system of buying a commission. Worked si well at Balaclava...