Mr. Short Rate Risin'

Mark Thoma points us to Tim Duy quoting Jon Hilsenrath at the WSJ:

Federal Reserve officials are on track to start raising short-term interest rates later this year ...

But maybe they've already started? I noticed something in my predictions that the monetary base had started to fall a bit below my counterfactual projection. What if we've seen 'peak QE'? So let's posit that the most recent value of the monetary base is the highest value it will attain -- and let's say it just stays there. Here's the 'peak QE' counterfactual (it doesn't really matter if you use the last point or the actual peak value):

In that case, trend economic growth will mean NGDP continues to rise -- which means short term interest rates will start to rise. Basically, if you think we've reached peak QE, then interest rates are already on the rise. Model is in blue, data in green and yellow:

The markets haven't caught on yet ... or maybe they think we haven't seen peak QE?

Powerful evidence for the information transfer model

I realized a bit after I posted this that putting the data on the graphs of the annual average rates of change in M0 vs the annual average rates of change in NGDP would be a powerful demonstration of the information transfer model. If the data fell in a triangle mapped out by the lines representing the rates of change of each variable, then that shows -- regardless of your belief -- that NGDP ~ k log M0 with k falling.

This is a thing of beauty:

The rainbow curves show the theoretical response of NGDP to changes in M0 for 1965 (purple) to 2015 (red) in steps of 10 years. The data are the annual average rates of change in NGDP vs the annual average rates of change in M0 for the same time period.

A pure quantity theory of money would show a line. A theory that based inflation or NGDP growth expectations set by a central bank (with a significant weight put on e.g. future expected inflation) would have a more complicated relationship that would depend on the exact sequence of shocks and announcements from the central bank. Needless to say, there is no reason for the data to fall in the triangle above in the pattern fading from purple to red along the lines predicted by the information transfer model (nothing prevents it from doing so, but in that case the expectations theory wouldn't have any more content than the ITM theory).

An expectations-based theory that put its weight entirely on past inflation could achieve a similar result simply because inflation and NGDP growth have been falling over time. (The simple martingale works, but doesn't really explain anything.)

The biggest reason Paul Krugman or Scott Sumner on seeing this graph wouldn't immediately abandon their views of how the economy works (and in fact, a lot of their prior education [1]) -- aside from the fact that isn't how knowledge progresses [2] -- is that they'd say the model is based on correlations observed in historical data. Well, 1) it isn't actually -- it's based on a set of propositions (axioms) and just happens to explain historical data and 2) this is weak tea -- all theories are based on past data. At least those theories that have some contact with empirical data [3]. Pure armchair philosophy reason tends to be (somehow) immune to empirical tests. Why accept the ITM? Because empirical success. Or keep to your angels and pin-heads [4].

Footnotes:

[1] The theory partially confirms the quantity theory of money and the IS-LM model, so some stuff gets to stay.

[2] Max Planck: A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. This is why I put out links on teh Twitters; for the kids.

[3] I once read this line and shuddered: I recall Bob Lucas and Ed Prescott both telling me that [empirical tests] were rejecting too many good models. 

[4] Sorry for the ranting bit at the end. I'm up against things like this: Since 2008 [market monetarists] been more accurate in our predictions than any other school of thought. How can you be accurate when there are no quantitative predictions? What on Earth does accurate qualitative analysis mean? 

Floating the Swiss Franc won't change the price level

Commenter Charlie Clark asked for a prediction from the information transfer model (ITM) after my post on Switzerland in the wake of abandoning its currency peg. I mentioned at the comment that the ITM would predict essentially a linear extrapolation from the price level curve that I had that contained data through the end of 2013, but said I would post a more concrete version as soon as I got the chance [1]. This is that post.

Actually, the prediction below uses the same data I used in the price level graph in the Switzerland post (i.e. up until the end of 2013 -- the exact end date was 2014.0, i.e. 01 Jan 2014). This means the result is a prediction of the data from the end of 2013 (i.e. 2014.0) through the end of 2015 (i.e. 2016.0) and we can see that the CPI data points from January 2014 to November of 2014 (the last available on FRED) are right on the trend line as predicted (shown in solid green):

The model is blue, and the data are green as usual on this blog. Here is year over year (YoY) inflation:

I use YoY inflation because I don't currently have seasonally adjusted data [2]. The model basically predicts an average of near zero inflation through the end of 2015. Like the initial pegging of the Swiss Franc in March of 2011, floating in January of 2015 won't have a major impact on the price level in the information transfer model -- except for the potential for market fluctuations.

Footnotes:

[1] One change from the previous price level fit was that I smoothed the monetary and NGDP data (like I first did here) in order to get a linear extrapolation of those datasets. However, that didn't change very much in terms of the original model result. I provide the original version as a reference.

[2] I dislike YoY inflation as a metric because e.g. a high inflation number could just mean that the data points at time t and time t-1 represent positive and negative fluctuations, respectively. I am working on an ARIMA filter so that I can do the seasonal adjustment myself in the future.

I strongly disagree with what you are talking about

As a companion piece to my post on some basics of the information transfer model, I'm going to list several things that strongly go against the mainstream of economic thinking ... again in a Vox-style explainer format.

Preferences are irrelevant most of the time to many macro variables

Individual preferences, and metrics for them like utility (or expected utility), are irrelevant to macroeconomic outcomes. This is not to say they are irrelevant to microeconomics. However, the essence behind using the 'information theory shortcut' is that a theory that accurately models preferences at the micro level is so complicated that the result isn't distinguishable from randomness. Yes, you can model the pressure of an ideal gas in a container by calculating accurately all of the collisions between atoms and the walls of the container (we'd make an analogy here between energy and momentum conservation and stable preferences -- the atoms 'want' to conserve energy and momentum), but the resulting list of velocities you'd get for every atom would follow a Maxwell distribution ... even if you started with all the atoms at one side of the container.

Microfoundations are irrelevant to macroeconomics most of the time

This is a somewhat stronger statement than the previous one. The fact that you can do a pretty good job of describing the macroeconomy with a few variables (output, price level, unemployment rate, interest rates, ... it really doesn't matter what you include as long as the length of this list is less than, say, a million variables) and that economies with the same values of these variables tend to be in the same situation means that microfoundations are irrelevant. Why? Let's say your model is really complicated, like one of the Fed's DSGE models that describes 10 variables. That places any given solution in a 10-dimensional space. Now the economy in the US is made of 100's of millions of individual agents. That represents a greater than 100,000,000-dimensional space -- and that's if people are 1-dimensional! In order for your 100,000,000-dimensional microfounded theory to map to a 10-dimensional DSGE model, large portions of your 100,000,000-dimensional space must map to the same point (or subspace) of your 10-dimensional space. In thermodynamics, your 6N dimensional problem, where N is the number of molecules ~ 10^23, maps down to a few dimensions (a small set of variables like temperature, entropy, pressure, etc).

In the information transfer model, we tend to map to 2-dimensional spaces and still have a lot of empirical success. That's why I say 'microfoundations are irrelevant' -- there appears to be a lot of dimensional reduction going on in macroeconomics.

Actually, this is similar to the Sonnenschein–Mantel–Debreu theorem where assumptions about the microeconomics end up having no macroeconomic implications -- but stronger.

You keep saying 'most of the time', why? And why is even this contrary to the economic mainstream?

During recessions, the assumption of information equilibrium seems to break down temporarily. Recessions themselves seem to be an emergent phenomenon (they wouldn't exist for an individual market and they would happen regardless of the specifics of economic agents' preferences in your micro theory). Stories like the babysitting co-op may describe real economic phenomena (mainly a 'story' about the quantity theory of money), but it isn't what is happening in a recession. The 'monetary' contraction in the babysitting co-op may trigger a recession (as appears to have happened in the run-up to the 2008 financial crisis), but it isn't a recession on its own.

Several aspects of the macroeconomy are emergent

Some macro effects don't even exist for the agents in the microeconomic theory, such as sticky prices, secular stagnation and the liquidity trap in the information transfer model. Therefore there is no story you can tell with individual agents that both a) are accurate and b) capture the effect. I'm sure economists can come up with just-so stories to arrive at just about anything, but that's because there aren't limits on stories. This emergence means that for some effects, this statement by Paul Krugman is incorrect:

But behind [the economic model] is a story about people doing stuff: investors selling the currency because yields are down, the currency falling until it’s so low that people figure it has nowhere to go but up.

There is no 'story' behind entropic forces that you can tell for an individual atom. An atom participates in diffusion or osmosis because of entropy (counting states), not from a physical force acting on it. A single molecule of glue isn't sticky. A single molecule doesn't have a temperature (or entropy).

Even the idea of a demand curve or a supply curve is emergent. An atom doesn't exert less pressure because of the diminishing marginal utility of extra volume and a single economic agent doesn't pay a smaller price for an iPad because of the diminishing marginal utility of extra iPads. We as an ensemble of economic agents will buy more iPads at a lower price than a higher one, holding demand constant.

What emphasizes this last point even further is that there are such things as Veblen goods and Giffen goods -- things that individuals will become more likely to buy (or consume more of) if the price goes higher. As an ensemble of agents -- with a sufficiently large basket of goods -- we will still follow the general concept of consuming more goods at lower prices and fewer at high prices.

Sticky prices have no microeconomic story

Although critical to macroeconomics as practiced by the mainstream, nominal rigidity (i.e. sticky prices) has no microeconomic story behind it. I mentioned this in the previous segment, but I thought I'd emphasize it a bit more. Menu costs and Calvo pricing are models that attempt to get the effect of sticky prices into a micro model, but there really isn't much stopping an individual from changing the prices at their own store or lowering their own wage. There is however an entropic force preventing all of us from making those changes.

Adding menu costs or Calvo pricing to the micro models is a bit like adding a 'diffusion force' to atoms.

The liquidity trap has no microeconomic story

I thought I'd call this one out, too. No, the liquidity trap has nothing to do with individuals lacking a preference between a zero interest government debt (at the zero lower bound) and zero interest currency. In fact, the liquidity trap has a gradual onset (not sudden at the ZLB) and has been steadily rendering monetary policy less and less relevant to macroeconomics.

As the number of dollar bills increases (and the size of the economy increases), a given dollar bill is simply more and more likely to be facilitating a transaction in a low growth market. The emergent concept here is an economic temperature that falls as more and more money is added to an economy. Large economies are 'cold' economies.

Where else am I going against the grain? ....

Added 1/18/2015: Exchange rates don't (always) measure inflation

I think this is the best way to introduce this one:

Scott Sumner: Tom, I like Jason, but he needs to learn how to explain his ideas to economists, using intuition. 100% of economists believe that inflation leads to currency depreciation. If you are going to argue the opposite you need a STORY, not just a model, or an empirical study.

That also goes to the idea about a story above. However, in this case, there actually is a story and it's that demand for currency is important, not just supply. In a liquidity trap, inflation and exchange rates appear to decouple. That is how e.g. Switzerland could depreciate its currency and get deflation.

As it is written, though, Sumner is still correct. Inflation leads to depreciation, but depreciation doesn't always lead to inflation.

Obscure references

The titles of the past two posts have a couple of obscure references, although one is less obscure than the other (at least to me; I have this feeling that no one under 30 has any idea who Steve Martin is).

I have no idea what you are talking about

This is a clip from TV Carnage (I think it is Casual Fridays) that has a cop with a very thick Canadian accent saying the line in question that's repeated a few times throughout the video. The creators of TV Carnage are Canadian themselves (with significant accents), but even they make fun of how strong his accent is.

The new CPI numbers are here! The new CPI numbers are here!

This is a reference to The Jerk:

I also made a couple of references to the theme song from the LEGO movie (NGDP is awesome), but that is not very obscure. It's hard to jazz this stuff up sometimes.

I have no idea what you are talking about

By far, the most common response to the work I've been doing on this blog from people with a background in economics is that they have no idea what I am talking about. It's nice being noticed by Scott Sumner, Nick Rowe, David Glasner and Stephen Williamson, but they all have said at one time or another they don't understand what this blog is all about. At least that's better than Noah Smith's response (deleting my comments**). Mike at Free Radical disagreed with the philosophical approach (I am skeptical that economics can tractably model human behavior). Robin Hanson thought I was using the word 'information' in a different way than I am (in the Shannon information entropy sense, not in The Market for Lemons or game theory sense). I'd say the major issues are my explanatory writing skills, my background in physics (I use the word isentropic way too much) and the lack of formal education in economics (I have worked my way through most of Romer's Advanced Macroeconomics, but all that has helped me to do is write the information transfer model as a DSGE model***).

So let me try to do another Vox-style explainer post ... on the right side of the blog there are a series of posts under the heading "Information transfer economics for beginners", so those are some more resources.

Where does the name information transfer economics come from?

It is based on the first title of this paper by Fielitz and Borchardt that I saw: Information transfer model of natural processes: from the ideal gas law to the distance dependent redshift. They have since changed from "information transfer" to "natural information equilibrium" and I have followed suit, more frequently referring to information equilibrium than information transfer. In that paper, Fielitz and Borchardt come up with a kind of generalized thermodynamics and connected a couple of different things in physics to information theory that hadn't been connected before. I derived supply and demand (or at least something that looks exactly like supply and demand diagrams) from their equations assuming demand was an information source and supply was an information destination. I thought that was pretty cool, so I started a blog to see if anything more could come out of it.

What does this have to do with information theory?

In truth, the information theory mostly serves as a motivation for a set of equations, and then the blog is mostly about the consequences of those equations. The equations the information theory sets up are for an abstract diffusion process. (In the model, money is like time and output is like distance.) I do sometimes go back to the information theory for insight -- for example observed prices will tend to fall below a theoretical maximum price because you can't get more information out of a signal than it contains.

Isn't your theory just the quantity theory of money?

Pretty much. Instead of writing $MV = PY$, I would write:

$$
\log PY \sim k \log M
$$

$$
\log P \sim (k -1) \log M
$$

The big difference is not only that $k$ changes (yes, like velocity), but changes deterministically. The deterministic formula for $k$ comes from the underlying information theory: it is a ratio of the Hartley information from two sets of given size. However, you can rewrite that ratio in an interesting way using the properties of logs. A set $A$ has $|A|$ elements and the Hartley function is 

$$
H(A) = \log_{b} |A|
$$

where the information is measured in units based on base $b$. Our deterministic $k$ above is

$$
k \sim \log_{M} PY
$$

[update 1/19/2015, so you don't have to dig at the link] or

$$
k \sim \frac{\log PY}{\log M}
$$

That's why I've called the changing $k$ the unit of account effect in the past. It represents the units which which we measure everything in economics ... and $PY$ is just NGDP. The proper money aggregate $M$ is determined empirically. It's not M2 or the monetary base. The answer turned out to be strikingly simple: physical currency.

Wait. If it's just the quantity theory, how do you describe Japan's price level so well?

Well, $k$ has a tendency to fall over time in economies because $M$ grows faster than NGDP (and NGDP has recessions). Eventually $k$ gets close to 1 (from above) and you have something that looks pretty much exactly like a liquidity trap.

What about inflation expectations?

This is where I have in the past gone full heterodox with all due respect to the field of economics. Expectations might be able to wiggle inflation around a bit, but in the end the price level comes from $k$ and $M$ through the equations above.

However, I have since lightened up on this and in fact consider one possible interpretation of the information transfer model is as information flowing from an expected future to a realized present. Instead of considering all possible levels of aggregate supply and aggregate demand consistent with a given price level, we consider all possible expected futures consistent with present macro conditions. That is still different from typical expectations models in economics. A credible central bank sets an inflation target and expectations will center around that target -- it determines $\pi_{t+1}$ from a model (e.g. the central bank can hit its target). In our case, we are agnostic about how expectations are set and take the result to be the average over the entire set of expectations consistent with macro conditions -- it determines $\pi_{t+1}$ from the set of all $\pi_{t+1}$ consistent with e.g. $\pi_{t}$, $m_{t}$, etc****.

This is like thermodynamics. The pressure of an ideal gas is the most likely pressure given its volume, temperature, etc. The actual value of pressure will vary -- but since there are so many molecules, the variance is small and you get a deterministic result. In the information transfer model, there are so many people with so many different inflation expectations that effectively, the final result depends entirely on how big $M$ is.

Where does the model differ from thermodynamics?

Probably the biggest difference is that there is no second law and in fact, a fall in entropy is linked to recessions. This is where human behavior matters. Humans can coordinate themselves in a way that atoms cannot. Most of the time humans are uncoordinated (maybe an economist would say coordinated by the market here), but sometimes we panic together and that results in a recession.

How deep does the connection with thermodynamics go?

Really deep. In fact, there may be a way to apply partition functions and define an economic temperature (proportional to $1/\log M$). Secular stagnation and liquidity traps may be emergent properties of economies that don't exist for individual markets -- so no amount of models that just put together separate markets will capture these emergent properties.

Are there more ordinary applications of this approach?

Yes. Here's an example of a two-good market that basically gets the standard result. And here's how to derive the ISLM model.

Additional questions?

Footnotes:

** It's his blog; he can do what he wants.

*** A neat takeaway is that the different information transfer index ($\kappa = 1/k$) limits drop out simply in the DGSE model. You get either a "liquidity trap" inflation = constant ($\kappa$ = 1) or "quantity theory" inflation = money growth rate ($\kappa$ = 1/2).

**** The $m$'s and $\pi$'s here are the log-linear versions of $M$ and $P$ such as you would see in a DSGE model.

The new CPI numbers are here! The new CPI numbers are here!

And it's not a surprise that core CPI inflation came in below 2%. Here's how the new data point looks with the model:

If PCE follows this number, I might be able to declare victory in at the end of January over the Fed NY DGSE model!

Solving the identification problem via information equilibrium

David Glasner mentions the identification problem as a rationale for disregarding the quantity theory of money (in the course of an otherwise interesting post on the uselessness of monetary aggregates for monetary policy). In my continuing effort to win Glasner over to this blog's approach to complex economic systems through information equilibrium -- which produces a theory that has the quantity theory as its high inflation limit (see here, here) -- I thought I'd target the identification problem.

The identification problem in economics, in its simplest form, is the statement that a series of changing prices cannot be uniquely identified as a series of moves along supply and demand curves (basically you can't get two slopes -- elasticities of supply, demand -- from a series of two variables P, Q -- the price and equilibrium quantity supplied).

In the information transfer/equilibrium model, the relationship between the price (P), supply (S) and demand (D) is given by

$$
P = \frac{dD}{dS} = \frac{1}{\kappa} \frac{D}{S}
$$

This relationship can be thought of as coming from a several different lines of argument (a tiny modification to an equation that appears in Irving Fisher's thesis, the simplest theory that obeys long run neutrality, or -- as Fielitz and Borchardt arrived at it -- an information equilibrium argument, including a temporal version). The information transfer index $\kappa$ appears as it does as a reference to Fielitz and Borchardt's original paper. This relationship allows you to derive supply and demand diagrams, holding either demand or supply 'constant' (I like to think of it as in contact with the supply and demand equivalents of a thermal bath).

The key to overcoming the identification problem is the fact that this equation has effectively one parameter ($\kappa$) from which both slopes (elasticities) of the supply and demand curves follow (see here and here). It is helpful to think of it as a 3D surface, like this one (in terms of NGDP, the currency component of the base and the price level):

Now the source of the identification problem helps you! As long as your data represents movement of both the supply and demand curves, the price measurements (samples of the LHS of the equation above) constrain the curvature of this 3D surface. And if they don't represent moves of both curves, well, you're back to the reduced form -- you're fitting just a supply or demand curve. The quantity supplied then gives you the relative level of the quantity supplied to the price (there is still an overall scale freedom -- if you moved the decimal place on every dollar, you haven't done anything).

The essence of how information equilibrium solves the identification problem is by relating the slopes of the supply and demand curves through $\kappa$.

In monetary economics, though, $\kappa$ changes -- which might make you think we've re-introduced the identification problem! And that would be true if you allowed $\kappa$ to be a general function. This is where information theory comes to the rescue again because $\kappa$ has a specific meaning. It measures the relative size of the information units for D and S, or in monetary economics, NGDP and 'the money supply'. Since a 'dollar' of NGDP (N) and a 'dollar' of money aren't equivalent units of information (especially at different times), we need to let $\kappa = \kappa (N, M)$. I admit the functional form I use is an ansatz (fancy word for guess) based on the definition of the information transfer index, but it works empirically and can be motivated through a thermodynamics-based approach:

$$
\kappa (N, M) = \frac{\log c \; M}{\log c \; N}
$$

In order to keep the identification problem from coming back, I kept this ansatz to a single parameter.

This changing $\kappa$ allows the model to behave like the quantity theory of money at times as well as demonstrate many properties of the liquidity trap at others. It isn't wishy-washy about it though: it specifically shows when each regime is valid ($\kappa \sim 1/2$ means the QTM is a good approximation and $\kappa \sim 1$ means something like the IS-LM model is a good approximation).

The other benefit of this model is that it solves the perennial problem of which monetary aggregate is relevant to inflation empirically -- we choose the aggregate that fits inflation best. And it turns out the answer is the simplest possible one: currency in circulation. Not M2, not MZM, not the monetary base (that includes central bank reserves).

The result is a darn good model not just for the US (the graph below uses smoothed inputs), but for Japan and other countries:

Switzerland depreciated their currency and still had deflation

The SNB pegged their currency to the Euro in order to devalue it, but they still had deflation (or really low inflation). It did move the exchange rate -- which Scott Sumner thinks is a sufficient indication is an indicator [Sumner disagreed with that characterization, however see here**] for looser monetary policy. 

However:

• Switzerland is in a liquidity trap
• Exchange rates don't have an immediate link to inflation

The SNB has decided to let their currency appreciate again after the devaluation failed to produce inflation or spur growth -- as would be predicted by a liquidity trap model.

** Sumner:

"BTW, Kuroda is engaged in monetary offset (the yen has recently fallen from 109 to 118)" 

I would say engaging in monetary offset is looser policy; tighter policy would stand to see a rise in the Yen.

Updated with footnote 1/15/2015 11:48 PST

Targeting NGDP is awesome (if only it worked)

NGDP is awesome
NGDP is cool when you're part of the team
NGDP is awesome when you're living your dream

Some slight edits to the theme song from The Lego Movie.

In the previous post, I agreed with Nick Rowe that NGDP level targeting is superior to inflation targeting. It's an obvious choice between targeting no recessions and targeting no deflation during a recession.

Well, unfortunately, the ITM is an existence proof of a model where both NGDP level targets and inflation targets eventually fail -- and it's a model that fits the empirical data quite well. That means it is decidedly not obvious the central bank can do "whatever it needs to do to ensure its previously announced target will be hit".

I used the path of NGDP vs M0 pictured at the top of this post (originally derived here) and plugged that into the price level model (see here) to show how the rate of money growth (money printing) affects the inflation rate (as well as NGDP and RGDP growth) -- and how that relationship changes over time.

Effectively, we have log P ~ k log M0, so the rate of inflation is proportional to the rate of money growth. However, k changes over time (it gets smaller) so that it takes a higher and higher rate of money growth to produce the same inflation rate. The result is a series of lines with decreasing slope from 1965 (purple) to 2015 (red):

A horizontal line appears at 2% inflation rate along with a diagonal line that shows a relationship P ~ M0. In yellow, I show the distribution of money growth rates over the same period (fainter means fewer year-long periods with that growth rate). There is a fairly sharp cutoff at around 10% (marked on the chart) -- the Treasury almost never prints more than 10% more money in a given year-long period. Now it is true that it is possible to get an inflation rate of 2% in 2015 (see the end of the red curve intersects the 2% inflation line). However that requires over 15% growth in M0 -- a rate not seen since WWII. 

This is why I think that central banks will eventually fail to meet inflation targets. They will be reluctant to print more and more money (in the case of the Fed, less likely to pass on banks requests for cash to be printed). That 10% value, across which the rate of printing is unprecedented, will act as a wall. It's not a hard barrier, so in principle a central bank could go right through it (as I've mentioned before here). Accelerating exponential growth in the money supply cannot be sustained indefinitely, however ... at a minimum you'd run into a logistic problem of printing physical currency.

This is not just a problem for inflation targets. NGDP targets also require accelerating base growth to sustain:

Again, the purple line is 1965 and the red line is 2015 and the ones in the middle go by steps of 10 along the rainbow. The yellow highlighted area are the typical values of currency growth. I've added the distribution of NGDP growth rates (in year-long intervals) in green. You can see how the rainbow curves span the intersection of the peaks of the distributions NGDP growth rates and the currency growth rates. What is interesting is that the rule P ~ NGDP is actually better on average over the post-war period than P ~ M0.

The line at 10% shows roughly the limit of achievable NGDP targets without printing unprecedented amounts of currency. Ironically, you could probably reach a 5% NGDP target in 2015 -- but that would become harder and harder without printing more and more money in the future.

Now that we have NGDP and inflation, we can show how RGDP growth falls over time if the central bank stays within its past performance (you read this graph the same way as the previous two):

This fall in RGDP growth has been shown before on this blog and in fact if you subtract this trend, you can discover RGDP growth is a stationary random process (it does not have unit root).

Now what would you expect would happen to the rate at which the central bank prints money if it was getting harder and harder to keep inflation (or NGDP or RGDP) where you want it? If it was getting harder and harder to steer your car so that it stayed on the road, you'd end up steering the wheel more and more in each direction to correct one way and then another. In monetary terms, you'd increase the rate at which you printed money and then rapidly decrease it -- the oscillations in the growth rate would get larger and larger. Guess what:

This picture reminds me a bit of a bifurcation fractal. It is the result of a central bank trying harder and harder to steer the economy. The good news is that these wild fluctuations don't have a large effect on the economy -- as we entered liquidity trap conditions, the effect of these oscillations become more and more muted.

An argument against all this is that the model is just fitting to past behavior and it can't be extrapolated to future moves from the central bank (or the economy). In part, this is the Lucas critique; it is actually somewhat more fundamental. Past empirical data may not capture the diversity of behavior. For example, if you've never seen a bird fly, your model for how a bird runs around on the ground could lead you to think it will be eaten by faster predators. This is always a problem with models and it is rare that your model leads to to believe some fundamentally new thing exists without it first being empirically observed (a few examples from physics are the positron, black holes and supersymmetry). The ITM does have some earmarks of such discoveries, though. It follows from a fundamental argument (in our case, information equilibrium; in the physics examples these are special relativity, general relativity and no-go theorems in quantum field theory, respectively), derives from a fundamental symmetry (in our case, long run neutrality of money; in the physics examples, the constant speed of light, the equivalence principle and Poincare symmetry, respectively), and it is highly empirically accurate in the range of empirically observed phenomena (well, supersymmetry hasn't been observed yet).

There are deep reasons to believe the ITM. These deep reasons might be incorrectly applied or totally off base, but they should at least be considered. 

For a some different views on NGDP targeting, see Scott Sumner, Tony Yates, Cullen Roche and Simon Wren-Lewis.