Cobb and Douglas didn't have changing TFP, and Is TFP entropy?

Continuing in this series (here, here and here), I found Cobb and Douglas's original paper from 1928 [pdf] where their least squares fit gives them the function:

$$
P = 1.01 L^{3/4} C^{1/4}
$$

And they get a pretty good result:

Also, Noah Smith writes today:

Yes, in a Solow model you can tie capital K to observable things like structures and machines and vehicles. But you'll be left with a big residual, A.

Now if we use the information equilibrium model:

$$
NGDP = A \; K^{\alpha} \; L^{\beta}
$$

And use the "economic potential" (see also here):

$$
NGDP = TS + X + Y + ...
$$

$$
NGDP \approx (c/\kappa + \xi + \eta + ... ) NGDP
$$

So that ...

$$
NGDP \approx (c/\kappa + \xi + \eta + ... ) A \; K^{\alpha} \; L^{\beta}
$$

$$
= (A c/\kappa + A \xi + A \eta + ... ) \; K^{\alpha} \; L^{\beta}
$$

$$
= (\underbrace{A c/\kappa}_{\text{residual productivity}} + \underbrace{A \xi + A \eta + ...}_{\text{measurable output}}) \; K^{\alpha} \; L^{\beta}
$$

or

$$
= (\underbrace{A c/\kappa}_{\text{entropy}} + \underbrace{A \xi + A \eta + ...}_{\text{real output}}) \; K^{\alpha} \; L^{\beta}
$$

So that we say

$$
NGDP \approx (A_{TS} + A_{0}) \; K^{\alpha} \; L^{\beta}
$$

Noah's statement is essentially that we expect a number the size of $A_{0}$, but it turns out it is large (i.e. the size of $A_{TS} + A_{0}$) and $A_{TS}$ is this large residual (or the whole term is the large residual). In this description, the Cobb Douglas production function works because the entropy term is approximately proportional to output: $TS \approx (c/\kappa) NGDP$.

The UK: another case of "productivity problems" where they don't exist

Brad Delong shows us another case where the framing makes us think of the UK economy as low productivity instead of just low NGDP. If we look at it in the same way we looked at the US and Mexico here, then we see there is no actual change in productivity and the Solow production function works quite well ...

The exponents of capital and labor are 1.0 and 0.51 respectively -- comparable to 0.9 and 0.51 for Mexico and 0.85 and 0.40 for the US.

Mathiness and the Solow production function

Mark Thoma sends us to Paul Romer's blog post about his paper that defines "mathiness" in economics research -- in particular in growth economics:

The style that I am calling mathiness lets academic politics masquerade as science. Like mathematical theory, mathiness uses a mixture of words and symbols, but instead of making tight links, it leaves ample room for slippage between statements in natural versus formal language and between statements with theoretical as opposed to empirical content.

I think there is no better place to see this than the Solow growth model's Cobb-Douglas production function. A really pure dose of the mathiness can be seen here at MR University. In it, they motivate the equation

$$
Y = A \; K^{\alpha} \; L^{1 - \alpha}
$$

where $Y$ and $K$ are real quantities. First, why are they real quantities? I've never quite found a good answer, but in general most economists think that the price of bread being twice as much as it was decades ago is something that should be adjusted for (taken out of the values), not a fundamental property of economics. Of course, solving that problem (by adjusting for inflation) creates a new problem -- money illusion (why do humans seem to think in nominal terms). Usually when incorporating an idea creates new problems, it's a sign that maybe the idea isn't right. But adjusting for inflation is well-established, so let's not rock the boat too much. Besides, there's other examples we can use.

Second, $A$ (total factor productivity, TFP) is introduced on the MRU videos as representing something that exists in the real world: "ideas" or productivity. It's not just a normalization factor. It also implies that it can change over time or across countries. We are immediately assuming that instead of an unimportant normalization that is constant over time, we have a critical component of growth economics.

Finally, while there are potentially reasons for the constant returns to scale assumption where the exponents of $K$ and $L$ add to 1 -- Alex Tabarrok states it in terms of doubling $K$ and $L$ should lead to a doubling of output -- it represents an additional assumption. In most cases, however, the reason for the assumption is a theoretical reason, not empirical.

Actually, we've made three major assumptions before comparing to empirical data: real quantities $Y$ and $K$, $A$ is a factor of production and constant returns to scale for $L$ and $K$. These assumptions lead to $A$ (the normalization factor in your original model) being the most important thing in growth economics -- it represents most of economic growth. Additionally, the model using these assumptions are used to make the assertion (explicitly in the MRU video, but generally the conclusion in much of growth economics) that Mexico doesn't use its labor or capital as effectively as the US.

Note that the theoretical assumptions create these new mysteries: 1) why is most growth TFP and 2) why do some countries use capital and/or labor better than others.

Now in the much more general information equilibrium approach, we end up with almost the same Solow production function

$$
Y = A \; K^{\alpha} \; L^{\beta}
$$

but without the three assumptions. $Y$ and $K$ could be nominal or real quantities, $A$ is a normalization factor that mostly represents the units of $K$ and $L$, and $\alpha$ and $\beta$ are completely arbitrary. What do we get if we compare this model to empirical data? Almost perfect agreement:

That's for the US and Mexico, using nominal quantities for $Y$ and $K$. $A$ is just a normalization factor and not responsible for any economic growth. In Mexico, $\alpha + \beta \simeq 1.42$ with $\alpha \simeq 0.90$ and $\beta \simeq 0.51$. In the US, $\alpha + \beta \simeq 1.25$ with $\alpha \simeq 0.85$ and $\beta \simeq 0.40$. We draw the exact opposite conclusion as MRU: Mexico grows much faster than the US for a given (relative) input of capital or labor!

This may even resolve another conundrum created by the Solow growth model -- why would the US or other advanced countries invest in Mexico if productivity was higher in the US? Sure, maybe the stock of capital is low and so you get more growth relative to depreciation -- but again that is entirely because of the way the Solow production function is built! In the information equilibrium framework, we see that increases in capital grow the economy a bit more than in the US (the exponent is 0.90 vs 0.85). Why move your labor intensive manufacturing to Mexico? Fractionally increasing labor in Mexico produces fractionally more output than in the US (the exponent is 0.51 vs 0.40). I am thinking that "productivity" may just be a way to preserve the idea that the US economy is the best in the world ... a way steeped in mathiness. And maybe even racism.

Note that making the overall normalization $A$ an important factor and using "real" quantities basically transforms the scale of the unit of account an important property of economic growth. The fact that it's ~ 100 Yen or ~ 10 pesos that is roughly equivalent to 1 US dollar or 1 Euro (completely arbitrary designations) is turned into an important economic fact about productivity -- at least if the information equilibrium view is correct.

If you look at the Solow production function empirically and scientifically, you end up with a pretty simple model that works remarkably well! If you try to add assumptions, you end up having to live with added mysteries and a much more complex model -- that doesn't even work that well. Call it Occam's razor, or call it rooting out mathiness. Just be curious -- why do we make certain assumptions?




Update +15 min: The rather large NGDP growth of Mexico in the 1980s is the result of hyperinflation. The nuevo peso was introduced in 1993, shaving off three zeros from prices. Also added the (relative) in the paragraph after the graphs.

Solow production function and nominal values

Editor's note: Still cleaning out my backlog of unfinished posts. This is a question I've had and is addressed to the economists out there ... even after reading through a couple macro textbooks, I still don't have a good answer. File under questioning whether real and nominal are actually useful concepts in economics.

As noted here, the Solow growth model Cobb-Douglas production function

$$
Y(t) = A(t) K(t)^{\alpha} \; L(t)^{\beta}
$$

works really well if $A = constant$, and $\beta \neq 1 - \alpha$ and both $K$ and $Y$ represent nominal values.

One thing I have not been able to understand is that when using real values in the traditional version with $\alpha + \beta = 1$, call them $Y = P(t) y(t)$ and $K = P(t) k(t)$, you end up with a factor of the price level relative to the nominal version ...

$$
y(t) = A(t) k(t)^{\alpha} \; L(t)^{1 - \alpha}
$$

$$
P(t) y(t) = A(t) P(t)  k(t)^{\alpha} \; L(t)^{1 - \alpha}
$$

$$
Y(t) = A(t) P(t)^{1 - \alpha}  K(t)^{\alpha} \; L(t)^{1 - \alpha}
$$

The extra factor of $P^{1- \alpha}$ could be absorbed by the $L$, but labor is given in terms of hours or people (or 'labor units'), not wages ... or is it?

The nominal version of the equation seems to make more sense (it is a combinatorial problem with dimensionless nominal dollar units and 'nominal' labor units).

The real version leads to the mystery of the fall-off in Total Factor Productivity (the 'great stagnation'), and TFP -- i.e. phlogiston -- being the majority of economic growth.

Editor's note, added 5/13/2015: Sounds like a no-brainer, but it requires re-thinking all the other instances of real vs nominal ... as I've addressed here. This post was an initial draft for the one at that link that I abandoned and restarted.

Real and nominal may actually be an attempt by economists to adjust for entropy terms. 

Money defined as information mediation

In the previous post I wrote that "macroeconomics does not currently know what money is or does". Instead of simply tearing down, I'd like to be constructive. In the information equilibrium framework money has a rather simple and mathematically beautiful explanation.

Let's start with an AD/AS model with aggregate demand (N) in information equilibrium with aggregate supply (S) with the price level (P) as the detector. We write this model in information transfer notation as:

$$
P : N \rightarrow S
$$

and the information equilibrium condition

$$
\text{(1) }\;\;\; P \equiv \frac{dN}{dS} = k \; \frac{N}{S}
$$

In general we can make this transformation using a new variable M (i.e. money):

$$
\text{(2) }\;\;\; P = \frac{dN}{dM} \frac{dM}{dS} = k \; \frac{N}{M} \frac{M}{S}
$$

If we take N to be in information equilibrium with M, which is in information equilibrium with S, i.e.

$$
P : N \rightarrow M \rightarrow S
$$

Then we can use the information equilibrium condition

$$
\frac{dM}{dS} = k_{s} \; \frac{M}{S}
$$

to show that equation (2) can be re-written

$$
P = \frac{dN}{dM} \frac{dM}{dS} = k \; \frac{N}{M} \frac{M}{S}
$$

$$
P = \frac{dN}{dM}\left( k_{s} \; \frac{M}{S} \right) = k \; \frac{N}{M} \frac{M}{S}
$$

$$
P = \frac{dN}{dM}  = \frac{k}{k_{s}} \; \frac{N}{M}
$$

$$
\text{(3) }\;\;\; P = \frac{dN}{dM}  = k_{n} \; \frac{N}{M}
$$

Where we've defined $k_{n} \equiv k/k_{s}$. The solution to differential equation (3) defines a quantity theory of money where the price level goes as

$$
\log P \sim ( k_{n} - 1 ) \log M
$$

In words, we've introduced a new widget that mediates the information transfer from aggregate demand to aggregate supply, which allows us to re-write the entire theory in terms of aggregate demand and the quantity of that widget (i.e. money).

One interesting side note -- if we consider non-ideal information transfer we have to combine the equations:

$$
\text{(4a) }\;\;\; \frac{dM}{dS} \leq k_{s} \; \frac{M}{S}
$$

$$
\text{(4b) }\;\;\; P = \frac{dN}{dM} \frac{dM}{dS} \leq k \; \frac{N}{M} \frac{M}{S}
$$

Since by equation (4a) the derivative $dM/dS$ is less than $k_{s} M/S$, so the replacement of the derivative is with a quantity that is greater than the derivative. Therefore, we don't have the bound and in general we have to allow

$$
\frac{dN}{dM}  \nleq k_{n} \; \frac{N}{M}
$$

That is to say, out of information equilibrium, the price level can be above or below the equilibrium value given by the quantity theory of money (as is observed) -- with disequilibrium on the supply side being key to above equilibrium inflation. Supply shocks (supply out of equilibrium with money) tend to lead to inflation (e.g. the oil shocks of the 1970s) while demand shocks (demand out of equilibrium with money) tend to lead to disinflation.

Update 5/13/2015:

A couple more observations:

• It is interesting that the information transfer index $k_{n}$, which becomes $1/\kappa$ in the price level model I use, is a composite of the indices $k/k_{s}$. The index $k$, representing a 'conversion factor' from aggregate supply to aggregate demand and the index $k_{s}$, representing the conversion factor from aggregate supply to money, should in a sense be of the same order -- meaning the index $k_{n}$ should be approximately ~ 1. Which is what we observe ($k_{n}$ seems to range from about 0.9 to 2.5, or $\kappa$ from 0.4 to 1.1).
• A liquidity trap economy has $k_{s} \approx k$, i.e. $\kappa \approx 1$, while a quantity theory economy has $k > k_{s}$, i.e. $\kappa < 1$.

Leeches, a rant

Editor's note: I didn't post this at the time ... but I was going through my backlog of unfinished posts and random ideas over my lunch break and found this to be pretty entertaining on a re-read. It's a bit unfair to macroeconomists, but if any of you out there are interested in my views on macroeconomics in one of my more bitter moods, this is a good one .... it's for entertainment purposes only. I generally think academic macroeconomists do a good job given the limited data -- it's a tough field!

Prescribing leeches. From Wikimedia commons.

A working macroeconomist reading [Keynesian proponents] Krugman and DeLong feels as a doctor would if the Surgeon General got up and said that the way to cure cancer was to draw blood using leeches.

That is David Levine, cited approvingly by John Cochrane.

I apologize in advance for what is basically a rant.

From my experience slowly learning the subject of macroeconomics, looking through the imported mathematical machinery, I would actually say that the current state of the art in macro is not just leeches, but abstract mathematical models of idealized leeches.

I have some advice that should apply all around -- to Krugman, DeLong, Levine, Cochrane, Samuelson, Sumner and every other macroeconomist: you do not understand your field very well. Sure, you understand it much better than I do or some random person off the street. But the sum total of macroeconomic knowledge seems to be effectively zero [the random person's knowledge seems to be negative on average]. I have been through a first year graduate textbook on macroeconomics. There is quite literally nothing in it on the subject of figuring out how an economy works. There are models of things that have results that may or may not reflect real economic behavior. There are collections of potential effects. Are they real? Who knows? Who cares? There are a couple of plots of data -- mostly to illustrate that the real world actually irrefutably violates the assumptions of the models. In the end, it is a math book that sets about solving different simplifications of a problem it made up.

It feels like studying Galois theory -- a topic from mathematics that seems to just exist to solve a single problem (why is there no quintic equation) for which there is no real-world application. Macro differs from string theory, about which many physicists have a similar opinion, in that string theory seems to be mildly concerned that it is supposed to be a physical theory of things that exist.

Keynes is like the application of leeches, huh? My own opinion is that the era of Fisher through Keynes and Samuelson is the era where the language of mathematics was introduced to economics. The study of the Great Depression is akin to the Cholera outbreak of the mid 1800's in London and its effect on epidemiology. That would put economics about 100 years behind medicine (not because it is backward, but because good data wasn't available). With that analogy, it should have felt to Levine as if the Surgeon General got up and said the way to cure cancer is to collect population data and do statistical analysis. Leeches would be more like going back to Hume.

One issue when you are immersed in a subject is that you tend to think of the current state of the art being comparable to the current state of the art in other fields. In general these things cannot be compared except by analogies ... and the problem there is that you are making analogies between things that are not understood.

But I'm going to do it anyway.

In the following, the word "know" is used in the sense that not only do all mainstream macroeconomists agree on the details, but that the formulation of the problem and its solution is effectively the same across textbooks. In physics, the details of the mechanism behind the Lamb shift are taught pretty much identically in every textbook and all physicists agree that it is a real effect with an uncontroversial empirical value. In that sense, physicists "know" the Lamb shift.

Macroeconomics does not currently know what money is or does

There are various theories out there about how money acquires value -- some involving the fact that fiat money can be used to pay taxes, others involving more social mechanisms, still others based on expectations of agents. There are current arguments in the literature about whether monetary policy has a strong effect on most economies (or just some economies) or not.

In medicine this is a bit like not understanding the function of food. I'm not talking about details like what kind of diet is best, but rather broad things like how (or whether) food provides energy.

An equivalent unresolved problem in physics is dark energy in cosmology. Dark energy behaves in a particular way in General Relativity (that's where it gets its name), but its microscopic origin is unknown. There are theories involving cancellation in the quantum fluctuations of elementary particles or that it results from properties of the string theory vacuum based on the so-called anthropic principle. It's basically a complete mystery that I'd say is on the level of money in macroeconomics. You'd hear a different story from different economists about the value of money much like you'd hear a different story from different physicists about the nature of dark energy.

Macroeconomics does not currently know what causes recessions or what they are

Some economists think that recessions a normal function of an economy. Some believe that they can be mitigated by government policy to great advantage.

If this were medicine, it would represent a state of the art that did not agree as to whether someone was actually sick or not. Is the illness doing what needs to be done to the body to eliminate inefficiency? Or should we give the patient a fever reducer?

I had a hard time coming up with a good physics analogy here. Should I use the hypothetical Unruh effect? Gamma ray bursts? Baryon asymmetry? The stong CP problem? High temperature superconductivity? Sonoluminescence?

But I've settled on the arrow of time. Some physicists think this is solved by entropy. However it doesn't make sense that the initial state of the universe (i.e. nearly uniform energy in the big bang) should be low entropy compared to today. In a sense, we have no real reason for time to flow in any particular direction and some fun results -- like quantizing the Wheeler-deWitt equation resulting in time dropping out of the model completely -- end up with a confused mess (or radical simplification, depending on your viewpoint).

...

Considering the unsolved problems in economics, leeches would actually represent a step forward from not understanding what food is or whether the patient is sick!

Homo economicus and the Platonic ideal

Ideal Platonic solid with a messy shadow

Richard Thaler has a new book out called Misbehaving: The Making of Behavioral Economics. He has a piece at The Upshot (NYT) where he describes how agents behave like Spock in most economic theories:

This illustrates an important problem with traditional economic theory. Economists discount any factors that would not influence the thinking of a rational person. ... 

Economists create this problem with their insistence on studying mythical creatures often known as Homo economicus. I prefer to call them “Econs” ... 

... economists are often happy to admit that most of the people they know are clueless about economic matters. But for decades, this realization did not affect the way most economists did their work. They had a justification: markets. To defenders of economics orthodoxy, markets are thought to have magic powers. 

There is a version of this magic market argument that I call the invisible hand wave. It goes something like this. “Yes, it is true that my spouse and my students and members of Congress don’t understand anything about economics, but when they have to interact with markets. ...” It is at this point that the hand waving comes in. Words and phrases such as high stakes, learning and arbitrage are thrown around to suggest some of the ways that markets can do their magic, but it is my claim that no one has ever finished making the argument with both hands remaining still. 

Hand waving is required because there is nothing in the workings of markets that turns otherwise normal human beings into Econs.

All good stuff! Very observational. You come away from this thinking how silly of those economists who don't use behavioral effects! At the end Thaler leaves us with this thought:

The field of behavioral economics has been around for more than three decades, but the application of its findings to societal problems has only recently been catching on. Fortunately, economists open to new ways of thinking are finding novel ways to use supposedly irrelevant factors to make the world a better place.

Wait ... it's been around for 30+ years and it's only recently catching on? Obviously this approach hasn't lead to quite as resounding a victory over Homo economicus as we've been lead to believe.

Also, because of things like the SMD theorem, the main way individual behavior can have an impact at the macro level is as a representative agent. Homo sapiens only has an effect if we all behave the same way.

What I think is happening here is that in most functioning markets humans appear to behave like mathematical constructs, but that is only because functioning markets behave like mathematical constructs. I wrote about the human-independent Platonic ideal shining through a month ago:

I think this actually solves a really tough philosophical problem. If humans have free will and don't behave perfectly rationally all the time, why does it seem that when markets are functioning properly, the mathematics of economics work so well -- as if they were atoms in an ideal gas? 

The physicist Eugene Wigner once referred to the "unreasonable effectiveness of mathematics in the natural sciences" ... functioning markets represent a common Platonic ideal -- something that can be described by mathematics.

This is not to say that behavioral economics doesn't have its place -- it definitely does! But the reason it's taken 30 years for behavioral effects to catch on is because the Platonic ideal does a good job in most situations. But at other times when our behavior is highly correlated -- by evolution or culture or cognitive biases -- the Platonic ideal disappears in the dark of the cave.

The economic allocation problem

I've done a little bit of site redesign changing out some of the graphics, the blog description and adding a set of random posts instead of popular posts to the sidebar. This post serves mainly as an explanation of the new diagram appearing in the upper right of this blog when viewed with a desktop browser (and appears schematically in miniature as the favicon).

Imagine supplying pints of blueberries to various stores (our "space" coordinate). Blueberries go bad if left on the shelf too long, so each unit of supply and each unit of demand represents a single square on space-time grid. A person shows up at store #4 (space grid point 4) at time t = 2 (time grid point 2) wanting to buy blueberries, represented on the grid as a white translucent box. If there are blueberries available (represented by a blue cube), then blue cube and white box match up and a transaction occurs. If not, the blueberries go to waste or some demand goes unsatisfied. Here is a basic picture:

This is an allocation problem where we are trying to match up the blue cubes with the white boxes. I labeled the blue and white boxes destination and source respectively because they represent an information source and an information destination ... what does this have to do with information you ask?

I'm going to simplify this picture a bit by saying the blueberries don't go bad ... so we can add up all the boxes along the time direction (integrate over time) like this:

This creates a bar chart that is essentially a probability distribution:

Matching these two probability distributions is the least restrictive constraint on the solution to the allocation problem. In communication systems, one effectively tries to build a channel that gets the distribution of symbols (e.g. letters in the English alphabet or binary 1's and 0's) right on the input side and the output side; this is the basis of information theory [1].

Now you can't sell blueberries if no one comes to the store to buy them, so any difference in the destination distribution (blue) from the source distribution represents a loss ... a loss of information available in the source distribution. In information theory, this loss can be measured via the Kullback-Leibler divergence (calculated in the graph). In general, I(destination) ≤ I(source). Assuming equality is called ideal information transfer or information equilibrium. It turns out to be equivalent to assuming ideal markets where there is no excess supply or demand -- the probability distributions are equal.

You may be asking where the price comes into this. Well, if the blue (B) and white (W) boxes stay the same, then the framework is completely agnostic as to what the price is. All we can say is that the price is some constant value, call it p0, that we'd have to measure empirically. But if the allocations change by small amounts dB and dW, we can look at how the price fluctuates with changes in supply and demand. In this framework, p = dW/dB ... the change in demand given a change in supply.

Now you can change some of the details, but the general principle of looking at the information in the distributions that solve the allocation problem -- and how they have to change when either the source or destination changes -- is the framework set up by the information equilibrium (information transfer) model.

The framework is a somewhat more general (i.e. less restrictive) take on utility maximization and search/matching theory where one tries to solve for the optimal allocation (more on that here).

Footnotes:

[1] Added 5/12/2015: Borrowing from Shannon (1948), the probability distribution of letters in English evolves as we add dimensions:

Symbol frequency in English (1D categorical distribution)

OCRO HLI RGWR NMIELWIS EU LL NBNESEBYA TH EEI ALHENHTTPA OOBTTVA NAH BRL

Trigram structure (3D categorical distribution, 3-symbol combinations)

IN NO IST LAT WHEY CRATICT FROURE BIRS GROCID PONDENOME OF DEMONSTURES OF THE REPTAGIN IS REGOACTIONA OF CRE

You can see that matching the distribution of English letters is a necessary, but not sufficient condition for creating sentences in English -- however it can be a sufficient condition to faithfully reproduce a message transmitted through your communication channel.

Exchange rates and monetary policy

I think one of the more practical things to come out of the information equilibrium model is the description of exchange rates. It is an incredibly simple model that effectively says that exchange rates have little to do with inflation or monetary policy, but are rather about aggregate demand in the two countries you are comparing. If my country's economy is booming and yours is flagging relative to long term trends, your currency is going to be cheap for me.

In the macro world, the fact that the US economy is doing better than Japan or the EU since the 2008 financial crisis means that both currencies are going to look depreciated. The QE undertaken by each country is going to be irrelevant except in the sense that it affects NGDP ... which it doesn't.

Scott Sumner disagrees:

You thought Japanese QE depreciated the yen?  That’s just your imagination.  You think QE recently caused the euro to depreciate?  You are hallucinating.  The dollar fell 6 cents on the day QE1 was announced, in March 2009?  That’s a coincidence.

It is your imagination -- or at least an interpretation of data based on a specific model. And the dollar falling is a market failure, not a coincidence.

The trend in exchange rates follows the relative trends in NGDP:

Today the Yen is 20% below the Dollar, the Euro is 10% below the Dollar and the Euro is almost 20% above the Yen compared to 2009.

Today Japan's NGDP is a little over 15% below US NGDP, EU NGDP is 10% below US NGDP and EU NGDP is about 10% above Japan's NGDP compared to 2009.

... basically in line with the simple information equilibrium exchange rate model.

[NGDP data from FRED and exchange rate data from Bloomberg]

I'm not sure Noah Smith understands the "physics envy" charge

Noah Smith starts his post on physics envy with:

I hear all the time that economists have "physics envy". This doesn't seem even remotely true. I'm not sure whether "physics envy" means that economists envy physicists, or that economists want to make physics-style theories, or that economists wish their theories worked as well as those of physicists. But none of these are true.

I don't think this captures what people mean by "physics envy" as applied to economists. The second one comes close, but the real charge that is being made is that macroeconomic theories are way too abstract and complicated given both the available data and how well the theories work at empirically describing the data.

The context of "physics envy" is evident in Noah's charge that macro data is uninformative. Yes, the macro data is uninformative ... if your theory is really complicated (as I've talked about before). You don't need graduate level mathematics (like the fixed point theorems used in proving the existence of Arrow-Debreu equilibria) when you can't really describe NGDP. Physics envy is one way to put it ... polishing a turd is another.

I think this post from Duncan Black aka Atrios nails it (Black has a PhD in economics himself). There is quite literally no reason for an economist to refer to the real numbers as ℝ or even refer to real numbers at all. To say x ϵ ℝ+ is pretentiousness compared to x > 0. That is physics envy. Orwell comes to mind [1] as well. In physics, there are reasons to refer to the set of real numbers ... the one loop correction to the anomalous electron magnetic dipole moment is ~ α/π. There is π, a transcendental number, right there in the formula. If an economist came out with an interest rate being ~ 1/π I would be suspicious.

That is what I think is meant by the phrase physics envy.

To be fair -- Noah himself doesn't appear to exhibit physics envy. He has two papers on his CV that are devoid of unnecessary mathematical abstraction for what they are attempting to describe. See here [pdf] (with some lovely long descriptive variable names) and here [pdf]. Maybe that is why he doesn't recognize it.

...

PS. There were two great developments in the history of mathematics: algebra and calculus. Algebra comes from commerce (the math of money and transactions happening in an abstract space of numbers, brought to Europe, especially Italy, via the Arabs -- hence the name from al jabr) and calculus comes from agriculture (the areas of land, the motion of the sun and planets). So I'm not sure this from XKCD that Noah links really gets these right. There should be two pyramids with physics and economics at the top of each and mathematics in the intersection. Money and physical reality are the two major drivers of mathematics and the mathematics that is actually developed tends to be constrained by this.

Footnotes:

[1] I am thinking of Politics and the English Language: "Bad writers, and especially scientific, political and sociological writers, are nearly always haunted by the notion that Latin or Greek words are grander than Saxon ones ...". x > 0 in the example is the simpler way to say exactly the same thing. Of course am guilty of a lot of things Orwell was fighting against; I have a bad habit of too many e.g.'s, i.e.'s and q.v.'s.