"You're wrong because I define it differently"

There is a problem in the econoblogosphere, especially among heterodox approaches, where practitioners do not recognize that their approach is non-standard. I'm not trying to single out commenter Peiya, but this comment thread is a teachable moment, and I thought my response had more general application. 

Peiya started off saying:

Many economic theories are based on wrong interpretation on accounting identities and underlying data semantics.

and went on to talk about a term called "NonG". In a response to my question about the definitions of "NonG", Peiya responded:

Traditional definition of the "income accounting identity" (C+I+G = C + S + T or S-I = G-T) is widely-misused with implicit assumption NonG = 0.

So Peiya was using a different definition. My response is what I wanted to promote to a blog post (with one change to link to Paul Romer's blog post on Feynman integrity where I realize the direct quote uses the word "leaning" rather than "bending"):

For the purposes of this blog, we'll stick to the traditional definition unless there is e.g. a model of empirical data that warrants a change of definition. Changing definitions of accounting identities and saying "Many economic theories are based on wrong interpretation on accounting identities" is a bit disingenuous. 

Imagine if I said you were wrong because I define accounting identities as statistical equilibrium potentials? I could say that there is no entropic force associated with your "nonG" term, therefore you have a wrong interpretation of the accounting identities. 

But I don't say that. And you shouldn't say that about the "traditional" definition of accounting identities unless you have a really good reason backed up with some peer-reviewed research or at least open presentations of that research. 

You must always try to "[bend] over backwards" to consider the fact that you might be wrong. Or at least note when you are considering some definition that is non-standard that it is in fact non-standard. In my link above, I admit the approach is speculative. I say "At least if [the equation presented] is a valid way to build an economy." I recognize that it is a non-standard definition of the accounting identities. 

Saying people misunderstand a definition and then presenting a non-standard version of that definition is not maintaining the necessary integrity for intellectual discussion and progress.

I've encountered this many times where people basically assume their own approach is a kind of null hypothesis and other people are wrong because they didn't use their definitions of their model. Even economists with Phds sometimes do this. However "You're wrong because I define it differently" is not a valid argument, and it's even worse if you just say "You're wrong" leaving off the part about the definition because you assume everyone is using your definition for some reason. The only people who can assume other people are using their definition are mainstream economists because that's the only way science and academia operates. The mainstream consensus is the default, and not recognizing the mainstream consensus or mainstream definitions is failing to lean over backwards and show Feynman integrity. 

Commenter maiko followed up with something that is also a teachable moment:

maybe by nature he is just harsher on confused post keynesians and more compliant with asylum inmates.

By "he" maiko is referring to me, and by "asylum inmates", maiko is referring to mainstream economists (at least I think so).

And yes, that's exactly right. At least when it comes to definitions. There are thousands of books and thousands of education programs in the world teaching the mainstream approach to economics. Therefore mainstream economic definitions are the default. If you want to deviate from them, that's fine. However, because the mainstream definitions are the default you need to 1) say you are deviating from them, and 2) have a really good reason for doing so (preferably because it allows you to explain some empirical data).

Update:

In my Tweet of this post, I said that in order to have academic integrity, you must recognize the academic consensus. This has applications far beyond the econoblogosphere and basically sums up the problem with Charles Murray (failing to have academic integrity because he fails to recognize that the academic consensus is that his research is flawed) as well as Bret Stephens in the New York Times (in a twitter argument) who not only failed to recognize the scientific consensus but actually put false statements in his OpEd.

Labor force dynamic equilibrium

Employment data comes out tomorrow and I have some forecasts that will be "marked to market" (here's the previous update). If the unemployment rate continues to fall, then we're probably not seeing the leading edge of a recession.

I thought I'd add a look at the civilian labor force with the dynamic equilibrium model:

In this picture, we have just two major events over the last ~70 years in the macroeconomy: women entering the workforce and the Great Recession (where people left the workforce). This is the same general picture for inflation and output (see also here). Everything else is a fluctuation.

We'll get a new data point for this series tomorrow as well, so here's a zoomed-in version of the most recent data:

...

Update 5 May 2017

Here's that unemployment rate number. It's looking like the no-recession conditional forecast is the better one:

Mathiness in modern monetary theory

Simon Wren-Lewis sends us via Twitter to Medium for an exquisite example of my personal definition of mathiness: using math to obscure rather than enlighten.

Here's the article in a nutshell:

Any proposed government policy is challenged with the same question: “how are you going to pay for it”. 

The answer is: “by spending the money”.

Which may sound counter intuitive, but we can show how by using a bit of mathematics. 

[a series of mathematical definitions] 

And that is why you pay for government expenditure by spending the money [1]. The outlay will be matched by taxation and excess saving to the penny after n transactions. 

Expressing it using mathematics allows you to see what changing taxation rates attempts to do. It is trying to increase and decrease the magnitude of n — the number of transactions induced by the outlay. It has nothing to do with the monetary amount.

I emphasized a sentence that I will go back to in the end. But first let's delve into those mathematical definitions, shall we? And yes, almost every equation in the article is a definition. The first set of equations are definitions of initial conditions. The second is a definition of the relationship between $f$ and $T$ and $S$. The third set of equations define $T$. The fourth defines $S$. The fifth defines $r$. The sixth defines the domain of $f$, $T$, and $S$. Only the seventh isn't a definition. It's just a direct consequence of the previous six as we shall see.

The main equation defined is this:

$$
\text{(1) }\; f(t) \equiv f(0) - \sum_{i}^{t} \left( T_{i} + S_{i}\right)
$$

It's put up on the top of the blog post as if it's $S = k \log W$ on Boltzmann's grave. Already we've started some obfuscation because $f(0)$ is previously set to be $X$, but let's move on. What does this equation say? As yet, not much. For each $i < t$, we take a bite out of $f(0)$ that we arbitrarily separate into $T$ and $S$ which we call taxes and saving because those are things that exist in the real world and so their use may lend some weight to what is really just a definition that:

$$
K(t) \equiv M - N(t)
$$

In fact we can rearrange these terms and say:

$$
\begin{align}
f(t) \equiv & f(0) - \sum_{i}^{t} T_{i} -  \sum_{i}^{t} S_{i}\\
f(t) \equiv & M - T(t) -  S(t)\\
K(t) \equiv & M - N(t)
\end{align}
$$

As you can probably tell, this is about national income accounting identities. In fact, that is Simon Wren-Lewis's point. But let's push forward. The article defines $T$ in terms of a tax rate $0 \leq r < 1$ on $f(t-1)$. However, instead of defining $S$ analogously in terms of a savings rate $0 \leq s < 1$ on $f(t-1)$, the article obfuscates this as a "constraint"

$$
f(t-1) - T_{t} - S_{t} \geq 0
$$

Let's rewrite this with a bit more clarity using a savings rate, substituting the definition of $T$ in terms of a tax rate $r$:

$$
\begin{align}
f(t-1) - r_{t} f(t-1) - S_{t} & \geq 0\\
(1- r_{t}) f(t-1) - S_{t} & \geq 0\\
s_{t} (1- r_{t}) f(t-1) & \equiv S_{t} \; \text{given}\; 0 \leq s_{t} < 1
\end{align}
$$

Let's put both the re-definition of $T_{i}$ and this re-definition of $S_{i}$ in equation (1), where we can now solve the recursion and obtain

$$
f(t) \equiv f(0) \prod_{i}^{t} \left(1-r_{i} \right) \left(1-s_{i} \right)
$$

This equation isn't derived in the Medium article (and it really doesn't simplify the recursive equation without defining the savings rate). Note that both $s_{i}$ and $r_{i}$ are positive numbers less than 1. There's an additional definition that says that $r_{t}$ can't be zero for all times. Therefore the product of (one minus) those numbers is another number $0 < a_{i} < 1$ (my real analysis class did come in handy!) so what we really have is:

$$
\text{(2) }\; f(t) \equiv f(0) \prod_{i}^{t} a_{i}
$$

And as we all know, if you multiply a number by a number that is less than one, it gets smaller. If you do that a bunch of times, it gets smaller still.

In fact, that is the content of all of the mathematical definitions in the Medium post. You can call it the polite cheese theorem. If you put out a piece of cheese at a party, and if people take a non-zero fraction of it each half hour, those pieces will get smaller and smaller but eventually there is nothing left (i.e. somebody takes the last bit of cheese when it is small enough). Which is to say for $t \gg 1$ (with dimensionless time) $X \equiv T + S$ because $f(t) = 0$ with $t \gg 1$. 

But that's just an accounting identity and the article just obfuscated that fact by writing it in terms of a recursive function. Anyway, I wrote it all up in Mathematica in footnote [2]. 

Now back to that emphasized sentence above:

Expressing it using mathematics allows you to see what changing taxation rates attempts to do.

No. No it doesn't. If I write $Y = C + S + T$ per the accounting identities, then a change in $T$ by $\delta T$ means [3]

$$
\delta Y =  \left( \frac{\partial C}{\partial T}+ \frac{\partial S}{\partial T} + 1 \right) \delta T
$$

Does consumption rise or fall with increased taxation rates? Does saving rise or fall with increased taxation rate? Whatever the answer to those questions are, they are either models or empirical regularities. The math just helps you figure out the possibilities; it doesn't specify which occurs (for that you need data). The Medium article claims that all that changes is how fast $f(t)$ falls (i.e. the number of transactions before it reaches zero). However that's just the consequence of the assumptions leading to equation (2). And those assumptions represent assumptions about $\partial C/\partial T$ (and to a lesser extent $\partial S/\partial T$). Let's rearrange equation (3) and use $G = T + S$ [4]:

$$
\begin{align}
\delta Y = &  \frac{\partial C}{\partial T}\delta T + \frac{\partial S}{\partial T}\delta T  + \delta T \\
\delta Y = &  \frac{\partial C}{\partial T}\delta T + \frac{\partial G}{\partial T}\delta T \\
\delta Y = &  \frac{\partial C}{\partial T}\delta T + \delta G
\end{align}
$$

And there's where we see the obfuscation of original prior. In the medium article, $f(0) = X$ is first called the "initial government outlay". It's $\delta G$. However, later $f(t-1)$ is called "disposable income". That is to say it's $\delta Y - \delta T$. However those two statements are impossible to reconcile with the accounting identities unless $X$ is the initial net government outlay, meaning it is $\delta G - \delta T$. In that case we can reconcile the statements, but only if $\partial C/\partial T = 0$ because we've assumed 

$$
\begin{align}
\delta Y - \delta T & = \delta G - \delta T\\
\delta Y & = \delta G
\end{align}
$$

This was a long journey to essentially arrive at the prior behind MMT: government spending is private income, and government spending does not offset private consumption. It was obfuscated by several equations that I clipped out of the quote at the top of this post. And you can see how that prior leads right to the "counterintuitive" statement at the beginning of the quote:

Any proposed government policy is challenged with the same question: “how are you going to pay for it”. 

The answer is: “by spending the money”.

Which may sound counter intuitive, but we can show how by using a bit of mathematics.

No, you don't need the mathematics. If government spending is private income, then (assuming there is only a private and a public sector) private spending is government "income" (i.e. paying the government outlay back by private spending).

Now is this true? For me, it's hard to imagine that $\partial C/\partial T = 0$ or $\delta Y = \delta G$ exactly. The latter is probably a good approximation (effective theory) at the zero lower bound or for low inflation (it's a similar result to the IS-LM model). For small taxation changes, we can probably assume $\partial C/\partial T \approx 0$. Overall, I have no real problem with it. It's probably not a completely wrong collection of assumptions.

What I do have a problem with, however, is the unnecessary mathiness. I think it's there to cover up the founding principle of MMT that government spending is private income. Why? I don't know. Maybe they don't think people will accept that government spending is their income (which could easily be construed as saying we're all on welfare)? Noah Smith called MMT a kind of halfway house for Austrian school devotees, so maybe there's some residual shame about interventionism? Maybe MMT people don't really care about empirical data, and so there's just an effluence of theory? Maybe MMT people don't want to say they're making unfounded assumptions just like mainstream economists (or anyone, really) and so hide them "chameleon model"-style a la Paul Pfleiderer.

Whatever the reason (I like the last one), all the stock-flow analysis, complex accounting, and details of how the monetary system works serve mainly to obscure the primary point that government spending is private income for us as a society. It's really just a consequence of the fact that your spending is my income and vice versa. That understanding is used to motivate a case against austerity: government cutting spending is equivalent to cutting private income. From there, MMT people tell us austerity is bad and fiscal stimulus is good. This advice is not terribly different from what Keynesian economics says. And again, I have no real problem with it.

I'm sure I will get some comments that say I've completely misunderstood MMT and that it's really about something else. But please don't forget to tell us all what that "something else" is. But the statement here that "money is a tax credit" plus accounting really does say, basically, that government spending is our income.

But with all the definitions and equations, it ends up looking and feeling like this:

There seems to be a substitution of mathematics for understanding. In fact, the Medium article seems to think the derivation it goes through is necessary to derive its conclusion. But how can a series of definitions lead to anything that isn't itself effectively a definition?

Let me give you an analogy. Through a series of definitions (which I have done as an undergrad math major in that same real analysis course mentioned above), I can come to the statement

$$
\frac{df(x)}{dx} = 0
$$

implies $x$ optimizes $f(x)$ (minimum or maximum). There's a bunch of set theory (Dedekind cuts) and some other theorems that can be proven along the way (e.g. the mean value theorem). This really tells us nothing about the real world unless we make some connection to it however. For example, I could call $f(x)$ tax revenue and $x$ the tax rate ‒ and adding some other definitions ($f(x) > 0$ except $f(0) = f(1) = 0$) and say that the Laffer curve is something you can clearly see if you just express it in terms of mathematics.

The thing is that the Laffer curve is really just a consequence of those particular definitions. The question of whether or not it's a useful consequence of those definitions depends on comparing the "Laffer theory" to data.

Likewise, whether or not "private spending pays off government spending" is a useful consequence of the definitions in the Medium article critically depend on whether or not the MMT definitions used result in a good empirical description of a macroeconomy.

Without comparing models to data, physics would just be a bunch of mathematical philosophy. And without comparing macroeconomic models to data, economics is just a bunch of mathematical philosophy.

...

Update 5 May 2017:

Here's a graphical depiction of the different ways an identity $G = B + R$ can change depending on assumptions. These would be good pictures to use to try and figure out which one someone has in their head. For example, Neil has the top-right picture in his head. The crowding out picture is the bottom-right. You could call the picture on the bottom-left a "multiplier" picture.

Update 6 May 2017: Fixed the bottom left quadrant of the picture to match the top right quadrant.

...

Footnotes:

[1] "And that's why I don't like cricket." [YouTube] 

This is basically equivalent to what is done in the Medium article.

[2] Here you go:

[3] If someone dares to say something about discrete versus continuous variables I will smack you down with some algebraic topology [pdf].

[4] I think people who reason from accounting identities seem to make the same mistakes that undergrad physics students make when reasoning from thermodynamic potentials. Actually, in the information equilibrium ensemble picture this becomes a more explicit analogy.

The reason for the proliferation of macro models?

Noah Smith wrote something that caught my eye:

One thing I still notice about macro, including the papers Reis cites, is the continued proliferation of models. Almost every macro paper has a theory section. Because it takes more than one empirical paper to properly test a theory, this means that theories are being created in macro at a far greater rate than they can be tested.

This is fascinating, as it's completely unheard of in physics. Nearly every theory or model in a physics paper would either be one of four things:

1. It's compared to some kind of data
2. It's predicting a new effect that could be measured by new data
3. It's included for pedagogical reasons
4. It reduces to existing theories that have been tested

I'll use some of my own papers to demonstrate this:

https://arxiv.org/abs/nucl-th/0202016

The paper above is compared to data. The model fails, but that was the point: we wanted to show that a particular approach would fail.

https://arxiv.org/abs/nucl-th/0407093

https://arxiv.org/abs/nucl-th/0505048

The two papers above predict new effects that would be measured at Jefferson Lab.

https://arxiv.org/abs/nucl-th/0107026

https://arxiv.org/abs/nucl-th/0509033

The two papers above contain pedagogical examples and math. The first has five different models, but only one is compared to data. The second is more about the math.

https://arxiv.org/abs/nucl-th/0508036

Finally in my thesis linked above, I show how the "new" theory I was using connects to existing chiral perturbation theory and lattice QCD.

Of course, the immediate cry will be: What about string theory! But then string theory is about new physics at scales that can't currently be measured. Most string theory papers fall under 2, 3, or 4. Maybe if all these macroeconomic models were supposed to be about quantities we couldn't measure yet, then you might have a point about string theory.

Even Einstein's paper on general relativity showed how it could be tested, explaining existing data, or how they reduced to existing theories:

Reducing to Newton's law of gravity

New effect: bending of light rays by massive objects.

Explaining Mercury's perihelion rotation

I'm sure there are probably exceptions out there, but the rule is that if you come up with a theory you have to show how it connects/how it could connect to data, other existing theories, or you say you're just working out some math.

In any case, if you have a new model that can or should be tested with empirical data, the original paper should have the first test. Additionally, it should pass that first test ‒ otherwise, why publish? "Here's model that's wrong" is not exactly something that warrants publication in a peer reviewed journal except under particular circumstances [1]. And those circumstances are basically the circumstances that occur in my first paper listed above: you are trying to show a particular model approach will not work. In that paper I was showing that a relativistic mean-field effective theory approach in terms of hadrons cannot show the type of effect that was being observed (motivating the quark level picture I would later work on).

The situation Noah describes is just baffling to me. You supposedly had some data you were looking at that gave you the idea for the model, right? Or do people just posit "what-if" models in macroeconomics ... and then continue to consider them as .... um, plausible descriptions of how the world works ... um, without testing them???

...

Footnote:

[1] This is not the same thing as saying don't publish negative results. Negative empirical results are useful. We are talking about papers with theory in them. Ostensibly, the point of theory is to explain data. If it fails in it's one job, then why are we publishing it?

[2] When I looked it up for this blog post, it looks like another paper demonstrates a similar result (about the Hugenholtz-van Hove theorem [pdf]) but was published three months later (in the same journal) that I didn't know about:

https://arxiv.org/abs/nucl-th/0204008

Updated finance fortune-telling

Here's an update to the S&P 500 model forecast (see here for the previous update and the title reference):

And here's an update of the 10-year interest rate forecast:

Looking more like the 2016 election bump will "evaporate".

Core PCE inflation = -1.7%?

Core PCE has been updated for March 2017. I think I'm going to wait for the revised data before I update the forecasts:

Can we see a Phillips curve?

The new core PCE inflation number for March comes out May 1st. In preparation for that, I was looking at the dynamic equilibrium model for PCE inflation and adding more shocks to see how well the data could fit. In the process, I noticed something odd/interesting:

These are all positive shocks to PCE inflation, but notice anything about the dates? Let me add NBER recessions on this picture:

Each recession is associated with a positive shock to PCE inflation that precedes it. The only exceptions are the early 2000s recession (for which there is a debate on whether or not it is a recession) and the early 1960s recession (where there isn't data). Actually, it is not entirely out of the question to add one for the early 2000s [1]. Since these shocks precede the recessions, they'll precede the shocks to unemployment (adding the dynamic equilibrium model of unemployment from e.g. here)

This reproduces a "Phillips curve"-like behavior. Inflation rises when unemployment has been falling for awhile after an unemployment shock. Just after a positive inflation shock, we get a shock to unemployment. Therefore inflation will tend to fall (since the shock is over) while unemployment is rising. These fluctuations are likely happening on top of the demographic transition of the 1960s and 70s.

If we are headed into another recession (per here), this might explain the higher inflation of the past year or so (core PCE inflation was over 3% in Jan of 2016 and 2017, having not been above 3% since 2012):

This is interesting as it means rising inflation is a sign of an upcoming recession (the center of the inflation shock precedes the center of the unemployment shock by about 1.3 years on average). However, this could be a just-so story. Inflation rises because unemployment gets low. But as recessions are random with roughly a mean time between them of about 8 years, it just appears we get recessions after unemployment has been falling for awhile (and we get a rise in inflation).

Update 1 May 2017

I had forgotten about the low CPI number earlier in April which should have prepared us for the very low March 2017 number: -1.7% (continuously compounded annual rate of change).

Footnotes:

[1] I don't necessarily think it's useful, but here it is:

High dimensional budget constraints and economic growth

This is something of a partial idea, a work in progress. Let's say there is some factor of production $M$ allocated across $p$ different firms. The $p$-volume bounded by this budget constraint is:

$$
V = \frac{M^{p}}{p!}
$$

p-volume bounded by budget constraint M

Let's say total output $N$ is proportional to the volume $V$. Take the logarithm of the volume expression 

$$
\log V = p \log M - \log p!
$$

and use Stirling's approximation for a large number of firms:

$$
\log V = p \log M - p \log p + p
$$

If we assume $V \sim e^{\nu t}$ and $M \sim e^{\mu t}$ and taking the (logarithmic) derivative (continuously compounded rate of change) and re-arranging a bit:

$$
\nu = \left(  p+ \left( t - \frac{\log p}{\mu} \right) \frac{dp}{dt}   \right) \mu
$$

Now let's take $p \sim e^{\pi t}$ and re-arrange a bit more:

$$
\text{(1) }\; \nu = p \left( 1 + \left(1 - \frac{\pi}{\mu} \right) \pi t   \right) \mu
$$

In the information equilibrium model, for exponential growing functions with growth rates $a$ and $b$ we have the relationship (see e.g. here)

$$
a = k b
$$

where $k$ is the information transfer index. So in equation (1) we can identify the IT index

$$
k \equiv p \left( 1 + \left(1 - \frac{\pi}{\mu} \right) \pi t   \right)
$$

In a sense, we have shown one way how the information equilibrium condition with $k \neq 1$ can manifest itself. For short time scales $\pi t \ll 1$, we can say $p \approx p_{0} (1 + \pi t)$ and:

$$
k \approx p_{0} \left( 1 + \pi t + \left(1 - \frac{\pi}{\mu} \right) \pi t   \right)
$$

This an interesting expression. If $\pi > 2 \mu$ then the IT index falls. That is to say if the rate at which the number of firms increases faster than the factor of production increase, then the IT index falls. Is this the beginning of an explanation for falling growth with regard to secular stagnation? I'm not so sure. 

As I said, this is a work in progress.

Update to the predicted path of NGDP

The new GDP numbers are out today, and RGDP came in a bit low per the dynamic equilibrium. However the NGDP number is basically on track [1] with the prediction started over two years ago (most recently updated here):

I added orange dots and an orange dotted line to show the data available at the time. It looks like we can pretty well reject the "old normal" exponential growth model (gray dashed in both graphs). In the second graph, the model NGDP growth rate (blue line) appears biased high by 0.2 percentage points compared to the linear fit to the data (dotted yellow line).

There are still potential revisions (see the difference between the orange dotted and yellow curves), so 26 May 2017 we'll get the second estimate.

...

Footnotes:

[1] Meaning the deflator was high, which it was at 2.2%.

What will the GDP number be tomorrow?

Menzie Chinn shows us the various estimates from GDPnow (Atlanta Fed), e-forecasting, and Macroeconomic Advisers

I thought I'd put a prediction out there using this model (which estimates RGDP per capita [prime age], so this includes an extrapolation from the model plus an estimate of the prime age population growth with the errors propagated from each but nearly all of the error is in the RGDP model by an order of magnitude). The result is (SAAR, chained 2009 dollars):

16,933.2 ± 63.9 billion dollars (1σ)

or

0.71 ± 0.38 % growth [1] ... i.e. 0.3% to 1.1%

Chinn tells us the Bloomberg consensus is 1.1%. Macroeconomic Advisers says 0.3%. GDPnow says 0.2%. The dynamic equilibrium model of RGDP per capita basically covers that entire spread. However, the dynamic equilibrium model has only two parameters (since were not in shock). That means that all the parameters of the GDPnow model or MA's model are getting you a just few tenths of a percentage point.

GDPnow seems to take into account the "low first quarter effect"; I wonder if MA does the same?

...

Update 28 April 2017:

The number is here and it is a bit lower than the model shows:

16,842.4

(+ 0.2 %)

which means Quarter/Quarter growth (that I show above) was 0.2% (and annualized is 0.7% which you might have seen in news reports e.g. here).

However, this is the advance estimate and there is a tendency for these to be revised (though it could be "low first quarter effect" mentioned above). So we'll see on 26 May 2017 what happens.

...

Footnotes:

[1] Quarter on quarter SAAR. Based on the not-yet-revised 16,813.3 billion number for Q4 2016.