This is frustrating me. People (e.g. the Atlanta Fed Macroblog, the St Louis Fed Economic Synopses (pdf)) still aren't getting it. What can I do to attract attention to my simple point? Think up some totally insulting inflammatory blog post title? Nope, that's not really me. I'm just going to try again. And use bold.
You can't test whether core inflation is a useful indicator for a central bank to look at just by seeing whether core inflation forecasts future total inflation (or whatever the bank is targeting). You can't test whether anything is a useful indicator for central banks to look at that way. Everything ought to look useless by that test, if the bank is doing it right. What you are testing is whether the bank is doing it right.
If a central bank is targeting (say) 2% total inflation at a (say) 2-year horizon, and if it's doing it right, then deviations of total inflation from 2% ought to be uncorrelated with anything that the bank knew 2 years ago. This means that nothing (i.e. nothing in the bank's information set) should forecast 2-year ahead total inflation, if the bank is reacting correctly to those indicators. Core should fail to forecast future total inflation. Total inflation should fail to forecast future total inflation. Trimmed mean inflation should fail to forecast future total inflation. Unemployment should fail to forecast future inflation. Everything should fail to forecast future total inflation.
This is an immediate implication of rational expectations (on the part of the central bank). The bank sets monetary policy, looking at the indicators in its information set, so that the bank's forecast of 2-year ahead total inflation is equal to the 2% target. Deviations of actual inflation from 2% are therefore forecast errors. Under rational expectations (on the part of the bank) forecast errors should be unforecastable from anything in the bank's information set. They wouldn't be rational if you could forecast errors.
When you look at correlations between core inflation and future total inflation, you are not testing whether core inflation is a useful indicator of future headline inflation that the bank should pay attention to. You are doing something quite different. If you do find a positive correlation between core inflation and future total inflation, it means one of three things: 1. the bank is not targeting total inflation; 2. The bank's target for total inflation has changed over time; 3. the bank is targeting total inflation, and the target is not changing over time, but the bank is getting it wrong, and isn't responding as strongly to core inflation as it should, and so is violating rational expectations.
Now, if you want to learn how to do it properly, go and read my old post.
Worthwhile Canadian Initiative 
“I don’t understand you, therefore you must be stupid.” That is how you are thinking right now, and it is the reason everyone is ignoring you.
That, and the fact that what you are saying is irrelevant to their point. Nobody is claiming that one measure of inflation is more biased than another. Look at the Y-axis of that Atlanta graph; it is RMS error, not bias. The variance of a forecasting measure is just as important as any supposed bias; I could forecast inflation with sunspots, and might not have any bias, but so what?
And that isn’t even the main point, which has to do with the X-axis. The units of this are the filtration (information set) used to make inflation forecasts, and what they show is that inflation is not a Markov process; you make better forecasts by considering more history. That is true regardless of the measure used to make forecasts, but it is much more true for headline than for core inflation. Thus, if you do want to make forecasts based on a restricted history, you should use core.
A couple of points:
1. The Fed does have a dual mandate, so something that is correlated with future inflation might be something that is correlated with the other part of the Fed’s mandate and therefore causes the Fed to deviate intentionally from its inflation target. In particular, I think the Fed took an opportunistic attitude toward inflation during most of the period being studied: in order to avoid producing unnecessary and undesirable effects on employment, it avoided aggressively pursuing its target and instead only resisted moves away from the target, while allowing random events to move inflation toward the target. Correlations with future inflation could represent the influence of such random events rather than failures of policy or changes in policy.
2. A central bank doesn’t have much control over the inflation rate at very short horizons, and it’s debatable whether it has complete control even at fairly long horizons. Something that’s correlated with future inflation might be correlated with the uncontrollable part. In particular, the predictive power of core inflation is interesting in that it may reflect something that the Fed can’t control at a short horizon but my be able to control at a longer horizon. (A 3-year inflation rate is going to include maybe a year of inflation over which the Fed has little control, averaged in with the later inflation which it arguably does control, but since its target is a rate rather than a level, the first year will bring up the average if the next 2 years are on target.) This could be useful to the Fed as an indicator of when it needs to tighten (or loosen).
This is an immediate implication of rational expectations
It’s interesting to contemplate the mindset in which this statement is equivalent to, “This is obviously true.”
Phil: I don’t think they are stupid. I just think they haven’t read my posts (almost certainly true). So I’m standing up, waving my arms around, and talking loudly to try to attract their attention!
It’s not about bias. It’s about R-squared (or any other measure of forecasting power). The R-squared of deviations of target variable from target on anything in the bank’s information set should be zero, if the bank is doing it right. Sunspots should be exactly as good as inflation, core inflation, or anything else. They should all look useless as forecasters.
It’s not about history. Unless the bank forgets stuff, its information set at time t should include its information set at time t-1, t-2, etc. No matter how much history you include in the information set, it should all be useless, both individually and collectively, in forecasting inflation, at the target horizon.
Andy:
1. Yes, the dual mandate might complicate things. Especially if the target horizon for unemployment were different from the target horizon for inflation. (Otherwise you could just make the target a weighted average of the squared(?) deviations from target.) But even with a dual mandate, whther we would expect a positive, negative, or zero correlation between current (core or total) and future inflation would depend on the model.
2. Yes, we shouldn’t be surprised if there’s a positive correlation between current and future inflation at very short horizons. But the way I test this for Canada, the Bank of Canada says it is targeting year over year inflation at a 2-year horizon. So there should be zero correlation between the latest CPI data, and the change in the CPI between 12 months to 24 months from now.
JW: It is obviously true that central banks ought to make rational forecasts when choosing monetary policy. And that’s what I am saying. Whether they do in fact make rational forecasts is something I want to test, and I use this method to test. If they do in fact violate rational expectations, I want to advise them of that fact, so they can improve their monetary policy.
Krugman weighs in: http://krugman.blogs.nytimes.com/2011/06/02/core-madness-wonkish/
Sorry Nick, I’m not getting it. So say Altig et al don’t understand the subtlety of what they’re doing by measuring inflation. Say they set money supply and lending rates based on whatever they measure and this line of action is flawed. What actually results from this?
In other words, yeah they might not “get it” but so what? What specifically are they doing wrong right now in terms of setting monetary policy, and what are the reasons and portents they have it wrong?
jesse: I don’t know (without running some regressions) whether the Fed has been getting it right, or whether the Fed should be looking at core, total, or a bit of both. I do know that the tests they are using for whether the Fed should look at core, total, or both, are wrong. For example, if core was a very useful thing for the Fed to look at, and if the Fed was looking at core, and responding correctly to core, their test would say that core was useless, because core would fail to forecast future inflation.
Damn. Maybe I’m still not saying it clearly enough!
I haven’t actually worked through all this, but is seems to me as though this was the whole point about the rational expectations econometrics literature. If people are incorporating all information, errors will be orthogonal to to the available information set. And here, all deviations of inflation away from target would be considered to be errors – and therefore uncorrelated with anything we observe now. Including, presumably, current core inflation. Econometricians could – in principle – use that orthogonality condition as a fulcrum to estimate a certain class of models.
Is that a restatement of your point, Nick?
Let’s say that the Fed doesn’t hit its target very closely over the relevant horizon. Either policy isn’t very effective, or they aren’t setting policy the way they say (or you think) they are. Either way, most of the variation in inflation is exogenous to policy. Then the method you’re criticizing would be fine, right?
So what makes you think that policy is sufficiently targeted, and sufficiently effective, over the relevant horizon, to exhaust the information content of past (core or whatever) inflation?
If the Fed was making systematic mistakes, then you’d get the correlation. But the absence of the correlation could simply be that those errors aren’t sufficiently strong/systematic to identify. And the issue appears to be an absence of correlation.
Stephen; “Is that a restatement of your point, Nick?” Yes. That’s a relief; Stephen understands me.
JW: suppose there were some potentially useful indicator X, that we knew the Fed was either unaware of, or for some reason was ignoring. Then we could indeed test whether X was a useful indicator by the simple method of seeing if X forecasts future inflation. But we know that the Fed is aware of core, and we think the Fed responds to core, so this simple test won’t work. If we did find that core nevertheless forecasted future inflation, that would mean that the Fed wasn’t responding to core strongly enough. But if core failed to forecast future inflation, that wouldn’t mean core was useless as an indicator. It might instead mean that the Fed is already exhausting all the information content in core.
Huh. Well then, I don’t see why this is so hard a point to get across. It seems that it should be perfectly straightforward. To those of us of a certain age, that is.
Maybe I’m missing it, but the crux of Bryan’s post is whether or not headline inflation, even if elevated for a year, can be a portent of runaway or elevated inflation in the medium term. That is, if someone like an OECD boffin points to headline inflation being high for a year and argues convincingly we should begin to get really, really worried that this is a permanent trend, Bryan is stating that, in fact no, the core inflation measure will still give you a better indicator of inflation in 2 years’ time. This is more a statement, timely stated I’m sure, that policymakers should put less weight on headline inflation than core when setting monetary policy because, at least insofar as past data can be used as future predictors, the core is still the right thing to track when trying to accurately predict averaged headline (and not necessarily core) inflation.
What I take away from his post is that measuring core is better than trying to second-guess headline inflation, even after a year of elevated headline inflation numbers and immense political pressure to raise rates.
Jesse: and I’m saying that is the wrong message to take away.
For example, suppose you found that headline inflation did not forecast future inflation, and that core did forecast future inflation. The message is not that the Fed should ignore headline and look at core instead. The message is that the Fed is already responding correctly to headline, by exhausting the information content of headline, but, at the margin, the Fed should respond more to core.
And if both headline and core inflation forecasted future inflation, at the targeting horizon, the Fed should respond more strongly to both.
(Unfortunately, they ran the regressions from 1985 to present. So you can’t really make any such judgements, because the target was presumably falling in the late 1980’s to early 1990’s. This method only really works if you look at data during a time when the target rate of inflation stayed constant.)
Nick, you are making some incredibly unrealistic assumptions about the ability of the central bank to control inflation — basically you are saying that the central bank can instantly control inflation with a random noise error term that is not serially correlated.
Let x_n = r_n – b_n, where r is the “natural” rate at time n, and b_n is the short nominal rate at time n. x_n would be the amount of steering. Suppose it takes time for the intervention to propagate:
Let I(n,k) = affect of steering by x_n on the inflation rate in period n+k:
1/2x_n in period n
x_n in period n+ 1
2x_n in period n+2
x_n in period n+3
1/2x_n in period n+4
0 thereafter
And suppose that the total inflation rate in period n is the sum of the influence of the current steering plus all the past steerings:
p_n = 1/2(x_n) + x_{n-1} + 2x_{n-2} + x_{n-3} + x_{n-4} + white noise
Now suppose that the objective of the CB is to minimize the running average deviation of inflation from 2%.
And assuming the CB cannot predict the natural rate but merely responds to observed changes in this rate, then because there are lags in the effect of the steering, the errors will propagate for 5 periods, with inflation below target for that time, even if the CB is doing the best job it can.
In that case, you will be able to predict future the future deviation from trend based on the past deviation from trend.
Now suppose that the natural rate cannot be observed, but other variables, {Z_i} can be observed — say output or employment:
x_n = b_n – f({Z_i})
In all cases, the CB does not try to predict the future variable, but merely responds to changes in current employment, etc, then because of the lags, it will appear that the Z_i is a good predictor of future inflation. And that would be a criteria to determine whether Z_i should be in the CB’s information set.
The Atlanta Fed is doing the correct analysis.
OK I’m going to go away and think about it. I’m familiar with a more scientific focus so this comes across to me as a control systems problem, with medium-term averaged headline inflation as the entity being controlled (I think). The setpoint of the controller is the inflation target. The question is what measures and estimators to use to make the system well controlled. Since their targeting policies have a lagging effect, they need the ability to estimate future inflation to determine the “effort” needed to maintain zero error, but also need to be aware their feedback measurements are not perfect. The question, posed differently, is should they be changing their control system, including their measures, to further reduce future error. This is a more difficult problem to analyze when the control loop cannot be “broken” and analysed open-loop.
So yes I agree the control loop is closed and this has implications for measuring the data. And I’ll think about it.
RSJ: “Nick, you are making some incredibly unrealistic assumptions about the ability of the central bank to control inflation — basically you are saying that the central bank can instantly control inflation with a random noise error term that is not serially correlated.”
No, I’m not saying that.
The Bank of Canada (which is explicit about its inflation target) says that it targets the year over year inflation rate at an 18 month to 2 year horizon. It is certainly not instant control. It is not even trying for instant control.
And, if it targets inflation at a (say) 24 month horizon, and has rational expectations, the error process should be an MA(23) process (using monthly data). None of this affects my statement that deviations of inflation from target should be orthogonal to the 24 month lagged information set, if the Bank is doing what it says it is doing.
jesse: I think that’s exactly the right way to think about it.
Nick,
No, the window over which the bank targets inflation is not the same window over which the steering terms have an effect.
The former is a policy variable whereas the latter is an endogenous variable.
The serial correlation of inflation will be determined by the endogenous window, not the policy window. Rational expectations is not some wand you can wave to make everything a markov process. If there are serial correlations in the endogenous variables, then there will be serial correlations in the error term, provided that the steering takes effect with a lag.
RSJ: the Bank of Canada is saying, in effect “Given our monetary policy instrument settings, and given the information we have available, we expect the inflation rate 24 months from now will equal 2%”. I am taking them at their word, and invoking the absolutely standard test to see if their expectations are rational — orthogonality of their forecast errors to their information set 24 months prior.
jesse: what I am saying here ought to be generalisable to any closed loop control system. You have a target variable (the room temperature) and a target (20C), and an instrument (the lever on the furnace) and a set of indicators (which would include the room temperature itself, the outside temperature, the windspeed, and lagged values of those same indicators), and a targeting horizon (you want to bring the room temperature to 20C in 5 minutes). There is an unknown optimal reaction function which sets the instrument as a function of the indicators. We know we have found the optimal reaction function when the room temperature cannot be forecast from the 5 minute lagged indicators and instrument. And if we observe a non-zero correlation between room temperature and lagged indicators or instrument, that tells us in which direction we need to adjust the reaction function to grope towards optimality.
“Given our monetary policy instrument settings, and given the information we have available, we expect the inflation rate 24 months from now will equal 2%”. I am taking them at their word,”
OK, the Cb can announce whatever policy it wants, but that doesn’t affect the endogenous lags, right?
I interpret these policy windows as measures that define the errors, not guarantees that the errors are not serially correlated. The CB cannot make such guarantees.
For example, a policy to minimize the variance between the moving average of inflation over a 2 year period and 2% will give a different measure of error then a policy to minimize the variance between the monthly average of inflation and 2%.
Nevertheless, neither of these two policies can promise that the errors are not serially correlated. One is a policy statement and the other is an economic statement about how changes to short rates propagate through to the rest of the economy. No CB policy position can affect that.
RSJ: The bank of canada targets inflation 2 years in the future. It does not target the average inflation rate between now and 2 years in the future. If it tries to target inflation at too short a horizon then it will run into problems, either excessive variance in employment, or “instrument instability” (where it has explosive oscillations in the instrument). But it says it can target inflation 2 years in the future. And yes, the errors will be serially correlated but only up to a 23 month MA process. That means the errors are still unforecastable at 24 months. MA and AR are different.
jesse (again) think of it as a meta thermostat, which adjusts for systematic errors in its own reaction function, by watching for past correlations between target and indicators.
Nick: if the bank were “doing it right” every move would incorporate all available information. So you wouldn’t be able to predict the next move from the previous one. Obviously that isn’t the case. Ie they don’t even pretend to be doing their best. Instead they grossly underreact (it’s a feature of agency and committee incentives that the cost of overreacting is much higher than the cost of underreacting), which is why the current deviation from target is a good predictor of the future deviation. Rating agencies have the same funny behaviour: if the current rating were their best estimate, howcome the last rating change predicts the direction of the next one?
So assume they’ll do little bits here or there and definitely try to do something if things really get out of hand. For the most part, assume they aren’t doing much. The evidence says it’s true.
“And yes, the errors will be serially correlated but only up to a 23 month MA process. That means the errors are still unforecastable at 24 months. ”
But they are forecastable. How do you explain that?
Or, let me turn this around:
Suppose you are deciding whether or not to take the CB at their word. What statistical test would you perform?
Nick,
you’ve ignored the most important point, made by Andy Harless. He said ” it’s debatable whether it has complete control even at fairly long horizons”.
I’ll go one further, in an open economy it is possible for a central bank to have no control over it’s inflation rate (even if that CB is not trying to maintain an exchange rate peg).
Here’s the examnple:
Imagine that their are only two currencies, the domestic currency called dollars and the foreign currency called globos. The idea here is that the entire world outside the domestic country has formed a currency union.
Further, suppose that goods trade is entirely frictionless. No shipping costs or anything to prevent arbitrage of different prices. Thus PPP holds perfectly all the time.
Finally suppose there is absolutely no capital movement between the domestic country and the rest of the world because while the rest of the world is allowed to hold dollars the domestic residents are forbidden from holding globos. Assume that somehow the capital controls are 100% effective.
Now suppose that the rest of the world pegs the nominal globo/dollar exchange rate unilaterally. Suppose that this peg is 100% effective (possible if the capital controls are 100% effective).
Now suppose the rest of the world chooses an inflation rate of -10% per year. That is, they choose 10% deflation.
PPP and the nominally fixed exchange rate mean that the domestic country also gets 10% deflation no matter what the CB does.
If the domestic country is unwilling to either put in their own controls on capital (which then prevents trade in goods since the foreigners can’t hold dollars) or somehow interferes in the goods market in another way (to break PPP) then they will have no control over their inflation rate at all despinte having complete control of the domestic money supply.
I should probably elaborate a bit more on how the example is supposed to work.
It might be wondered how the domestic central bank can print unlimited amounts of dollars without causing inflation somewhere, perhaps not domestically but in the foreign economies.
The mechanism would work as follows:
If domestic prices failed to fall in line with foreign prices then dollars would flow out of the domestic economy. Maintaining the exchange rate peg then forces the foreign authorities to absorb the dollars.
Now, to do this they may well have to issue globos and buy the dollars so how do they maintain their deflation? Well, they then have to tighten monetary policy some other way, higher interest rates or reserve requirements (maybe eventually exceeding 100%) which takes the globos back out of circulation.
The net effect of this sequence of actions is that the dollars have effectively been confiscated. That’s why I said they “may” have to issue globos to buy the dollars. The might just directly confiscate the dollars.
Either way, any time the domestic price level tries to move above the foreign price level the goods market arbitrage that enforces PPP will cause all the extra dollars to flow out of the domestic economy where they are simply confiscated and taken out of circulation by the foreign authorities.
The domestic central bank is then powerless to change the domestic rate of inflation through monetary policy.
Adam: By chance, I had just finished reading your blog post before checking in here. (Nice clean thought-experiment, by the way, which really clarifies things. You just need to add a vacuum cleaner in the foreign country to make it really clean, Ugh! That pun was not intended!).
In your thought-experiment though, the whole question of whether the central bank should look at core vs total becomes moot. It doesn’t matter what it looks at, because it can’t do anything. So the inflation target cannot be credible, whatever it does.
yes, but of course the real world is somewhere in the middle. The point was that the CB may have a lot, but not complete, control of inflation. This then admits the possibility of them doing everything right, as in doing the best they can, and still having forecastable errors.
Adam: thinking through your thought experiment some more, I come up with the “What happens when an unstoppable force meets an immovable object?” question. See my comments on your blog.
Adam: But in the real world, were talking about a CB that’s missing by a percent or two. If they have any control at all, they have the power to affect inflation by a percent over a three year horizon. If they move rates by, say 10% or so, I’m pretty sure they’ll even outdo themselves. Instead, they always underperform. And anyways, it’s not a constant bias; it’s a failure to react to foreseeable changes in both directions.
Or maybe, they underperform because they are targeting the asymptote, and the positive serial autocorrelation, is just the residual of shocks that haven’t fully dissipated. If the process has some second order behavior (inertia), they’d have to overshoot to get zero autocorrelation at some particular interval.
Nick,
This reminds me of your monetary policy as a thermostat post. I think I get it, but just to be sure let me throw at you the following scenario. Say the central bank is only using core inflation as its indicator variable to which it responds in order to hit a 2% headline inflation target two years from now. If the central bank is doing its job well, then core inflation should not be correlated with future headline inflation. Core inflation, however, should be negatively correlated with the instrument of monetary policy. That is, because the central bank is doing its job so well, it must be systematically responding to changes in core inflation so that there will be no deviation from its headline inflation target.
Does that sound right? Thanks.
So in a perfect world, the Fed (and Altig) would be looking at an indicator that doesn[‘t work, but in the world we have, the Fed is looking at a useful indicator. So the issue we ought to care about is whether the Fed accurately understands the imperfections, if any, with which it must deal.
Altig’s charts suggest that the imperfections we have make core CPI a good guide for policy.
jesse: what I am saying here ought to be generalisable to any closed loop control system. You have a target variable (the room temperature) and a target (20C), and an instrument (the lever on the furnace) and a set of indicators (which would include the room temperature itself, the outside temperature, the windspeed, and lagged values of those same indicators), and a targeting horizon (you want to bring the room temperature to 20C in 5 minutes). There is an unknown optimal reaction function which sets the instrument as a function of the indicators. We know we have found the optimal reaction function when the room temperature cannot be forecast from the 5 minute lagged indicators and instrument. And if we observe a non-zero correlation between room temperature and lagged indicators or instrument, that tells us in which direction we need to adjust the reaction function to grope towards optimality.
Oh dear Nick. No. Really, no.
Let me put my Engineering hat on and go to work.
Closed-loop systems feed the output back into the input. With negative feedback, the control makes the output convergent to the input, with some error. How well the control actually achieves this is a property of how the control is constructed, whether it is first or second order, system tolerances, etc.
The actual input to the control is the error after the feedback reference, not the raw inflation input itself.
The key is that we can observe both the output and the input to see how well the control is functioning. Error in this case is simply the opposite of efficiency.
We live in the real world, error is always present and efficiency is always less than 100%.
Furthermore, core inflation is not orthogonal to total inflation. Since core inflation is a subset total inflation, it is subject to the same control transformation as the other total inflation components. Now, if we deconstruct the Fed’s inflation control mechanism and compare a core-to-core system, we should get a similar function with different proportionality. If we think of the Fed as using a second-order Proportional-Integral-Differential controller, the Proportional term will change but the ID parts should be the same.
What the Fed is doing is measuring the error and efficiency of their target with respect to core inflation. Fine. I would quibble with the fact that the input is core and output it total, which is only a partial match. They ought to be comparing apples to apples, so core to core, or total to total unless they have ample justification for their choice, which should be rigorously documented.
“We know we have found the optimal reaction function when the room temperature cannot be forecast from the 5 minute lagged indicators and instrument. And if we observe a non-zero correlation between room temperature and lagged indicators or instrument, that tells us in which direction we need to adjust the reaction function to grope towards optimality.”
I disagree it necessarily “tells us” much. It MAY tell us something but there is also a chance that we are reacting to noise, which would make the system inherently less stable. The heating a room analogy is a good one and I’m not stating this because I have some engineering background. The analogy is that we are heating a room with a big furnace but the furnace applies heat unequally to different parts of the room. Our one “core” thermostat on the inner wall measures the temperature as (say) 20C but right beside the heating vent by the “fringes” it will be higher than 20C. My old gran sitting beside the vent thinks it’s too hot and asks me to turn down the heat. But my thermostat still reads 20C so… what to do to appease my old gran? The question to ask is whether I should add a couple of extra thermostats in other parts of the house to get a better idea of what’s going on, and that would adjust the effective setpoint, putting slightly less weight on my “core” reading and more weight on my “fringe” readings.
The bank is saying, well, yes people will get hot but we know based on the irrevocable laws of thermodynamics that if the fringes stay hot for a super long time, this will eventually start showing up in the core and the control effort from the furnace will commensurately decrease. When this happens they expect the fringes to cool down faster (because they’re closer to the exterior walls) and the overall average to be maintained. In other words, fringe temperatures are inherently more volatile. So the question in my mind is, if they do start considering the fringes, will this make the system more or less controllable? If it turns out that the fringes self-correct because someone opens a window or puts their foot on the vent, or that the sensor is in a high airflow region and produces many false positives I would argue it’s not. And the bank is effectively stating this: only having one thermostat is fine because historically the fringes will take care of themselves. Maybe they can do better by measuring other things too but, historically, they don’t have to in order to fulfill one of their mandates.
And Determinant (LOL) is right that there should be error in the system, both due to noise (in fact noise is often required to keep a system stable), and due to actual price movements. According to control systems theory, if inflation is on the move there must be non-zero “tracking error” (the difference between setpoint and measured) and this error will generally increase as the second derivative of CPI (i.e. the change in the inflation rate) increases.
Thanks for your patience. Hopefully some “orthogonal” thought helps gel some ideas for us.
Another point is that while adding more “fringe” weight to adjusting monetary policy may increase controllability, it also means the control effort may need to be adjusted more frequently. This has some broader implications and unknown consequences. If the Fed is seen as adjusting things quickly and in increments that are either too large or too spaced out, they may cause more problems than they solve. This is analogous to using a digital controller. Imagine we are controlling a furnace but can only adjust the temperature in increments of 0.25 degrees and only every 3 months. If that’s the case, there is more chance the system will end up less stable because of quantization errors. So there is some impetus to only track slowly changing events that have proven to be controllable given the time between updates and the minimum step size. On this front we’re in some ways lucky that most of the economy pretty much takes care of itself because the alternative could mean more frequent policy changes. But that’s another topic.
Does anybody know how to turn off italics?
David Beckworth: Yes, if core is the only indicator the Fed follows, and if it is responding to core correctly, there should be a negative correlation between indicator (core) and instrument, and a zero correlation between headline inflation and (lagged) core, and also a zero correlation between headline inflation and (lagged) instrument.
Determinant: “We live in the real world, error is always present and efficiency is always less than 100%.”
Obviously. Inflation will not stay exactly at 2%, because the Bank does not have a crystal ball. But if it is responding optimally to the (imperfect) information that it does have, those fluctuations in inflation will be orthogonal to that (lagged) information set.
You lost me on the rest. I think you are forgetting the lag/targeting horizon. The BoC targets 2 year ahead inflation.
jesse: “I disagree it necessarily “tells us” much. It MAY tell us something but there is also a chance that we are reacting to noise, which would make the system inherently less stable.”
Agreed. The zero correlation between target variable and one particular element in the information set is a necessary, not a sufficient condition. But remember that the instrument is also part of the information set. If the instrument were reacting to irrelevant noise, there would be a non-zero correlation between the target and the 5 minute lagged instrument, which also violates the orthogonality condition. Set monetary policy to the roll of a die, for example, and there will be a non-zero correlation between the die and future inflation, and between the monetary policy instrument and future inflation. Which tells us that monetary policy is responding too strongly to the die.
In the example with your gran, you are mixing 2 separate questions: what is the target variable; and what is the (set of) indicators we use to help us control that target variable.
(I’m not spending as much time as I would like responding to comments. All 4 of us WCI bloggers are at the CEA meetings today, tomorrow, and Sunday. So that’s all for now.)
test.
No Nick, I’m invoking basic control theory to say that your original hypothesis is incorrect. Looking at it through this lens provides a vastly different perspective.
I’m throwing rational expectations out the window and rephrasing the question. Nobody is perfect; we work with that we have. Rational expectations is an unrealistic assumption that Engineering, more used to dealing with the real world doesn’t use. I’m assuming the control mechanism does not change with time; all control theory assumes this.
One wishes to compare the usefulness of a subset of total inflation, one with less total noise, to control total inflation. Fine.
See this page on what a closed-loop control looks like: http://en.wikipedia.org/wiki/Closed-loop_transfer_function
I can feed core inflation in and look at total inflation coming out. Time invariance of the control function lets me do that.
This is the difference between the economics and the engineering mindset. Engineering looks first at the plumbing to see what’s possible. We see what process we will use, what errors are likely and can be tolerated and go from there to get the best result we can. Economics wants to get a perfect transformation from set 1 to set 1 and doesn’t care about the plumbing. Then whet you get error or imperfection complaints start to pile up.
From an engineering standpoint of control theory, rational expectations is an entirely unrealistic assumption. I’ve seen this difference before when I mentioned Ben Graham and his anticipation of index funds. My rebuttal then was that process matters. In engineering process matters. Index funds didn’t exist in the 1940’s because the concept of mutual funds was still new. Vanguard sold its product in the 1970’s on the basis of low management expenses using the existing retail mutual fund model. That couldn’t happen without the existence and performance record of actively managed funds. The process of getting there matters.
Or to put it another way:
You want a control to use a specific rule and adapt perfectly to any given information set such that there is no systemic error. You can’t have a rules-based system without systemic errors.
Well, Krugman doesn’t seem to have your type of problem with it.
Rational expectations is about expectations.
What the Fed can or cannot do is a question of capacity.
If the best the Fed can do is control inflation with serially correlated errors, then rational expectation will expect serial correlation of errors.
Central Bank announcements and policy targets are about politics and marketing.
By combining all three, Nick is arguing that we are in a wonder-world in which CB marketing must be matched by capacity, because Nick believes the marketing, and because of rational expectations, he must be right, therefore the capacity must be there.
It is so sneaky it is funny.
Which is why I asked whether a rational person should believe the CB or not, and how they could tell whether they should.
Suppose we don’t all take the CB at their word?
Thanks RSJ.
The engineering mindset does not sit well with marketing. We look at capacity and couldn’t care less about marketing. Engineering education is all about analyzing and optimizing capacity.
A little OT, since it wasn’t Nick’s point but the macroblog graph is confusing me: core is headline with noise removed. So, when using each as an estimator, shouldn’t we expect their RMS error to converge as we increase the sample size? Intuitively, the noise ‘comes out in the wash’. If that’s the case, I’m really not getting what the original St. Louis Fed is on about. It’d be news if headline and core didn’t converge something like 36 months out, but they do. So all is well, right?
“you are mixing 2 separate questions: what is the target variable; and what is the (set of) indicators we use to help us control that target variable.”
The goal is to control headline inflation (average room temperature), no? That never changed. Certain pockets are experiencing high levels of inflation and are beating the drum to do something about it (i.e. my gran). What is up for question is what measurements to make to improve the system. As I stated previous, coming from a control engineering perspective, yes we possibly can control the system better with more variables but we don’t have to. Monitoring the core is enough and the data back this up. Whether or not this is due to expectations is a separate discussion. We need not dissect the inner workings of the machine, which includes “expectations” to observe that inflation, both core and averaged headline, is well behaved under current policy.
@Patrick, the Fed is under immense pressure to raise rates based on headline inflation. The Fed’s post was an attempt to explain why they don’t have to react to recent upticks in headline inflation.
Have a great weekend.
I didn’t get that the St Lous Fed piece was defending core. I could be wrong. Maybe they’re just using Fed speak or I don’t speak no good english … but if Altig and the St. Louis Fed guy are both looking at the same data and coming to different conclusions … Yikes.
RSJ: Let me accept your model:
“And suppose that the total inflation rate in period n is the sum of the influence of the current steering plus all the past steerings:
p_n = 1/2(x_n) + x_{n-1} + 2x_{n-2} + x_{n-3} + x_{n-4} + white noise”
But make one change. Replace the white noise shock by a shock that is partly forecastable 3 periods ahead. For example, the shock could be an AR(1) process.
You (I mean “you” because my arithmetic is cr*ap) will now be able to solve for the optimal reaction function x(t) = R(x(t-1), x(t-2),x(t-3), x(t-4), shock(t)) that makes E[p(t+3) conditional on Information at time t and earlier] = 0% (or 2% or whatever). And you will also find that the deviations of inflation from the target will be an MA(2) process, and that p(t) will be uncorrelated with any variable dated (t-3) or earlier. That means the bank can target inflation at a 3 period horizon.
You will also find that if the bank tries to target inflation at a 1 period horizon it isn’t really feasible, because this will lead to explosive oscillations in x(t). (I think you will get the same thing if it tries to target inflation at a 2 period horizon as well).
Then, maybe, you will see what I am talking about.
“Replace the white noise shock by a shock that is partly forecastable 3 periods ahead”
Yes! Then you would be right. But I am assuming that shocks are not forecastable by the CB, which is why in my model I argued that the CB reacts to the decision variables as they are revealed, rather than before they are revealed.
This is how actual control processes work. You do not get to leap ahead of time. To the best of my knowledge, neither the current recession nor the housing downturn was forecast by the CB, neither was the oil embargo, etc.
So it again boils down to capability versus marketing. On what basis should we believe that the CB is capable of forecasting shocks? We can look back at previous Fed meeting minutes and see what they were worried about — I believe the concern du jour prior to the crisis was a collapse in the value of the dollar.
Now maybe I am wrong, and the CB is able to forecast shocks and that CB inflation errors are not serially correlated. I am open to that. But at least a case needs to be made — it’s a non-obvious assertion that requires evidence, right? And even if this is true for a period of time, what would guarantee that it would continue to hold in the future?