Saturday, April 22, 2017

Good ideas do not need lots of invalid arguments in order to gain public acceptance

There's a certain vein of economic criticism that has a tendency to turn me right back into a defender of the mainstream status quo. An example of it was written by Kate Raworth and published a couple of weeks ago in the Guardian. Prof. Raworth begins by saying modern economics is born of "physics envy". To some degree this is true (Irving Fisher's thesis advisor was the physicist Willard Gibbs), but really modern economic methods were born of the incredibly useful Lagrange multiplier approach that had its first applications in physics but is far more general. It basically provides a way of figuring out the optima of a function given complex constraints. In fact, it is so general, it's used in just about every scientific field including Raworth's ideal of evolutionary biology. Here's an example that took me a few seconds of Googling:

From Evolutionary Biology, Volume 27
edited by Max K. Hecht, Ross J. MacIntyre, Michael T. Clegg

Raworth comments:
Their mechanical metaphor sounds authoritative, but it was ill-chosen from the start – a fact that has been widely acknowledged since the astonishing fragility and contagion of global financial markets was exposed by the 2008 crash. ... So if the economy is not best thought of as a mechanism that returns to equilibrium and follows fixed laws of motion, how should we think of it? Like the living world: it’s complex, dynamic and ever-evolving.
As I just showed, this "mechanical" metaphor also applies to evolutionary biology and ecosystems sometimes collapse so there goes that argument. I'd bet that there are a lot more examples if Raworth wanted to look into this more than not at all. Maybe her enthusiasm comes from some sort of false belief that evolutionary biology doesn't have a lot of math in it?

Her comments also reference the 2008 crash as if this somehow invalidates anything about mainstream economics. In order to say the 2008 crash could be foreseen, prevented, or mitigated for certain using an evolutionary economics "gardening" [1] approach  requires a much more established and validated evolutionary macroeconomic theory than exists today. It's a bit like asking physicists why they didn't understand the solar neutrino problem before SNO and saying the answer is obvious but not providing any details of the requisite neutrino oscillation theory and evidence supporting it [2]. This issue with Raworth's "secret theory with secret evidence that supports it" reaches its zenith (nadir?) when she says:
The most pernicious legacy of this fake physics has been to entice generations of economists into a misguided search for economic laws of motion that dictate the path of development. People and money are not as obedient as gravity, so no such laws exist.
Either she has a secret theory with secret evidence, or has a time machine enabling her to see the future where this was either proven or humans all died off without finding them. More likely she is just repeating one of the age-old criticisms of science. "This system is too complex for your silly math" (or really that God/Zeus/whoever couldn't be constrained by human mathematical laws) was the same criticism leveled at the founding practitioners of science. People looked at nature and saw a mess; people did not believe it could be understood with simple laws and instead went with mythological explanations that used their intuition about human behavior. Thales was one of the earliest known people to say that nature may well be messy, but it might be amenable to rational argument. Imagine if people had listened to an ancient Greek version of Raworth saying "nature is complex, so mathematics and geometry will be useless". 

Following Thales example, I refuse to listen to Raworth's completely unsupported claim that no laws of macroeconomics exist. I've called claims like Raworth's the "failure of imagination fallacy" (but is also known as an argument from incredulity). It is odd that this total pessimism can come from the same source as the unbridled (and unsupported) optimism for the evolutionary approach.

Like most scientists, I would totally get on board with "evolutionary economics" if it had some useful results or evidence in its favor. But paraphrasing Daniel DaviesGood ideas do not need lots of invalid arguments in order to gain public acceptance.

Again, I've discussed this before with regard to David Sloan Wilson.


[1] Any time I hear the economist as gardener metaphor, it makes me think of this:

[2] For those that might have difficulty following my convoluted physics metaphor, the solar neutrino problem is the financial crisis, SNO is the experiment that eventually confirms whatever theory of the financial crisis is correct, and Raworth's evolutionary economics purports to be the confirmed neutrino oscillation theory. Raworth and other evolutionary economics proponents have not provided any evidence (or any theory for that matter) that their approach is useful or empirically accurate e.g. by showing they could prevent/mitigate/forecast the financial crisis before it happened or really explain any aspect of macroeconomic data at all.

Friday, April 21, 2017

Economics to physics phrasebook

Cameron Murray tweeted out his old post about economics terminology. Someone commented adding a sociology-economics dictionary. I thought I'd get in on the game with an "economics to physics" dictionary (the $^{*}$ means we're using the economics definition):

\text{Economics} & Physics \\
\text{commodity} & \text{matter} \\
\text{comparative advantage} & \text{coupling state spaces changes equilibrium}\\
\text{discount factor} & \text{smooth cutoff regulator} \\
\text{DSGE} & \text{arbitrary stochastic difference equation} \\
& \text{with constraints} \\
\text{demand} & \text{unobservable field that interacts with supply}^{*} \\
\text{endogenous} & \text{not an external field} \\
\text{equilibrium} & \text{solution to set of equations} \\
\text{general equilibrium} & \text{solution to all of the equations} \\
\text{partial equilibrium} & \text{solution to a few of the equations} \\
\text{estimate} & \text{fit parameters to data} \\
\text{Euler equation} & \text{equation of motion for constrained Lagrangian} \\
\text{exogenous} & \text{external field} \\
\text{expectations} & \text{toy model}^{*}\;\text{of the future} \\
E_{t} & \text{time translation operator} \\
\text{EMH} & \text{Brownian motion as an effective theory of prices} \\
& \text{(scale unclear)} \\
\text{inflation} & \text{rate of change of the price level}^{*} \\
\text{price level} & \text{arbitrary linear combination of prices} \\
& \text{(varies)} \\
\text{economics} & \text{theoretical economics} \\
\text{growth economics} & \text{theoretical economics} \\
& n \gg 1, t \gg 1 \;\text{quarter} \\
\text{macroeconomics} & \text{theoretical economics} \\
& n \gg 1, t \sim 1 \;\text{quarter}  \\
\text{microeconomics} & \text{theoretical economics} \\
& n \sim 1, t \ll 1 \;\text{quarter}  \\
\text{natural rate of interest} & \text{unobservable field} \\
\text{model} & \text{toy model} \\
\text{toy model} & \text{handwaving} \\
\text{theory} & \text{philosophy} \\
\infty & \text{sometimes inexplicably has units} \\
\text{growth} & \text{exponential growth} \\
\text{money} & \text{toy model}^{*}\;\text{of money} \\
\pi & \text{inflation}^{*} \; \text{, not}\; 3.14159...\\
\text{total factor productivity} & \text{phlogiston} \\
\text{rational expectations} & \text{causality violating toy model}^{*}\;\text{of the future} \\
\text{recession} & \text{toy model}^{*}\;\text{of a recession} \\
\text{supply} & \text{observable field} \\
\text{utility} & \text{unobservable field}

Housing prices over the long run (are we in a boom?)

Kevin Drum has a piece at Mother Jones (H/T David Anderson) that posits we are in the midst of another housing boom in the US, calling it the second biggest on record according to the Case-Shiller index. [Update: Brad DeLong comments on Drum, proposing a boom, bust, overshoot, rebound mechanism discussed below.] Now I've previously looked at the index using the dynamic equilibrium model (see also this presentation), but only back to the late 70s because that was what was available on FRED. Using Shiller's data from his website, we can now go back to the late 1800s.

Drum uses "real" values, adjusting for inflation. This creates some issues if your measure of inflation is mis-matched with respect to your nominal values (as described in an example here, and see addendum below), so we're going to focus on nominal values.

First, Drum seems to be correct about the boom ‒ assuming that we returned to the long run dynamic equilibrium, we should be at a much lower level (in everything that follows, blue is the model and yellow is the data):

In the second graph we show the 9 shocks that best describe the data (7 booms, 2 busts):

The two busts are associated with the Great Depression (1930.0) and the Great Recession (2008.5). Also of interest ‒ the Great Recession was twice as bad for housing prices as the Great Depression (in relative terms): 0.34 vs 0.78. The equilibrium rate of growth in the absence of shocks is ~ 1% per year.

According to the model, the latest boom appears to be ending, being centered in 2014.0 with a duration (width) of 1.5 years (think of this as the two-sided 1-sigma width of the Gaussian shock). It is not the largest boom in relative size (actually the smallest, but comparable to the 1917.9, 1970.0, and 1986.7 booms). However, with only the leading edge of the boom visible in the data, the duration and size are somewhat uncertain:

Going back to David Anderson's tweet up at the top, my own anecdotal evidence confirms this second boom as housing prices in the Seattle area have increased dramatically. Some other observations:
  • It does not appear that any housing booms are necessarily unsustainable. Out of seven booms, there have been only two busts. And the only two busts were during the Great Depression and Great Recession. While it may be that the housing bubble contributed to the latter, that leaves a sample of one on which to base conclusions like "unsustainable housing boom causes recessions when they bust". In fact, of the three largest booms, only one was followed by a bust.
  • In the absence of shocks, housing prices increase at about 1% nominally per year meaning that in the absence of shocks, housing would naturally become more affordable if wages kept up with inflation. It is housing price booms that make housing unaffordable.
*  *  *

Addendum: Inflation

Shiller deflates his housing prices by the consumer price index (all items). If we apply the above analysis to his data, we find a roughly similar structure:

Update + 3 hours: forgot the inflation rate graph.

However there is no CPI bust accompanying the Great Recession like for the Great Depression. Also, CPI has a shock in 1974 likely due to the oil crisis. That leaves us with 8 shocks (7 booms, 1 bust):

As you can see, the centers and durations (σ in the figure below) are mis-matched, yielding the fluctuating effect discussed in this post when you subtract the inflation shocks from the nominal housing price shocks:

Of the 7 shocks that match between the nominal index and the CPI index, all have some serious mismatch with the closest match being the 1970/1969 shock:

Center [y] (duration [y]) (size/amplitude [rel])

  1917.9 vs 1917.5 (1.7 vs 1.2) (0.3 vs 0.5)
  1930.0 vs 1930.5 (1.7 vs 3.4) (0.3 vs 0.5)
  1945.8 vs 1945.5 (3.1 vs 3.4) (0.9 vs 0.4)
  1970.0 vs 1969.4 (1.8 vs 1.8) (0.2 vs 0.2)
  1978.0 vs 1979.8 (3.0 vs 2.2) (0.8 vs 0.5)
  1986.7 vs 1989.7 (1.6 vs 4.4) (0.3 vs 0.3)
  2004.8 vs 2004.2 (5.4 vs 4.8) (1.3 vs 0.1)

These mis-matches yield fluctuations in the "real" price index (I am showing 4 cases = 1917, 1970/69, 1978/79, and 1986/89):

In fact, the latter two are close enough together that they combine into a series of two booms and two busts (in the real data) when in fact they are just two booms (in the nominal data and cpi):

The net effect is to make it look like the 1970s boom and the 1980s boom were followed by busts when neither the nominal price index nor the CPI have "busts". Another way to put this is that (in nominal terms) 1 boom + 1 boom = 2 booms + 2 busts (in real terms).

Therefore it is questionable whether the real housing price is the best measure during shocks. Outside of shocks, the real housing price shows how much housing increases relative to inflation (i.e. most goods and some fixed income). In fact, the dynamic equilibrium shows CPI grows at about 1.5% per year. This means that real housing prices in the absence of shocks decrease at about 0.5% per year (note that gold's nominal price decreases at about 2.7%). This is apparent in Drum's graph of Shiller's data in the periods between the booms. Combining the above descriptions of the nominal price index and the CPI, we have a (remarkably good) model of the real Case-Shiller index:

Note that the real index lacks a strong visible shock for the Great Depression (!) (the period from 1917 to 1945 shows relatively stable housing prices) whereas in the nominal index, it is one of the only negative shocks. 

Because the above model for the nominal index sees the most recent boom ending, we should see a return to the 0.5% decrease per year. But again, figuring out the size of booms and busts before they occur is generally difficult and fraught with uncertainty (for example, see these estimates of the unemployment rate ‒ the model appears to under-predict at first, then over-predict so we should probably take this as an under-prediction of the size of the current boom).

Update 22 April 2017

Brad DeLong comments on Drum's article, saying that we might be experiencing a rebound from too far of a collapse post-financial crisis. Now it doesn't appear that the pre-2000s housing bubble equilibrium has been restored:

We're still a ways above that, so is seems unlikely. However, if part of the 2000s housing bubble was sustainable, then it is possible:

This does lend itself to an overshoot, bust, undershoot, and return equilibrium picture. However it requires an ad hoc decomposition of the 2000s bubble into a "sustainable" and an "unsustainable" component. And there is insufficient data (only 2 busts: the Great Depression and Great Recession) to start making up theories for complex decomposition/dynamics involved in a boom-bust cycle.

The simpler model (with independent booms and busts) also says something similar ‒ a flattening of nominal housing price increases and a return to the (dynamic) equilibrium of 1% increase per year. Therefore Occam's razor should come in to play again: the simpler explanation is better ... at least until we get more data.

Thursday, April 20, 2017

Growth regimes, lowflation, and dynamic equilibrium

David Andolfatto points out how different models frame the data:
What does Bullard have in mind when he speaks of a low-growth "regime?" The usual way of interpreting development dynamics is that long-run growth is more or less stable and that deviations from this stable trend represent "cyclical" mean-reverting departures from trend. And if it's "cyclical," then it's temporary--we should be forecasting reversion to the mean in the near future--like the red forecasting lines in the picture below. ... This view of the world can lead to a series of embarrassing forecast errors. Since the end of the Great Recession, for example, you would have forecast several recoveries, none of which have materialized.  ... But what if that's not the way growth happens? Suppose instead that growth occurs in decade-long spurts? Something like this [picture]. ...
The two accompanying pictures are here:

As you can see, interpreting data depends on the underlying model. I've talked about this before, e.g. here or here. Let's try another!

What about dynamic equilibrium (see also here)? In that framework, we have a shock centered in the late 70s that hits both NGDP per capita (prime age) and the GDP deflator:

At this resolution, there is another shock to NGDP alone (although it might be visible in the deflator data, see here, but it's not relevant to the discussion in this post). Note: I am talking about quantities per capita (prime age) so it should be understood if I leave off a p.c. in the following discussion. The figure shows the transition locations as well as the width (red). The NGDP p.c. transition is much wider than the deflator transition. Combining these (dividing the NGDP p.c. model by the deflator model), you get RGDP per capita:

The lines represent the "dynamic equilibrium" for RGDP p.c. made from the dynamic equilibria for NGDP p.c. minus the GDP deflator. I translated it up and down tot he maximum and minimum during the period as well as for recent times. You can see how the interaction between two Gaussian shocks of different widths give you an apparent fluctuating growth rate, which is what Bullard/Andolfatto see in the data:

It's actually just the mis-match between the NGDP shock and the GDP deflator shock (likely due to women entering the workforce) that makes it look like different growth regimes when in fact there is just one. If the shocks to each measure were exactly equal, there'd be no change. Therefore it is entirely possible these "growth regimes" are just artefacts of mis-measuring the price level (deflator/inflation) data ‒ that a proper measurement of the price level would result in no changes (since NGDP and the deflator would be subject to the same shocks).

In fact, a LOESS smoothing (gray solid) of the RGDP growth data (blue) almost exactly matches the dynamic equilibrium (blue) result during the 70s and 80s:

In this graph the gray horizontal lines are at zero growth and the dynamic equilibrium growth rate (1.6%,  equal to the dynamic equilibrium growth rate of NGDP = 3.6% minus the dynamic equilibrium growth rate of the deflator/inflation = 2%). We can see that we were at the dynamic equilibrium in the 1950s and the early 2000s as well as today. The other times, we were still experiencing deviations due to the shock. 

I also show Andolfatto's 10-year annualized average growth rate (gray dotted), which basically matches up with a 10-year shifted version of the LOESS smoothing.

I'd previously talked about Bullard's regime-switching approach here. In that post, I showed how the information equilibrium approach reverses the flow of the regime selection diagram. But I also talked about how the information equilibrium monetary models can be divided in to "high k" and "low k" regimes (k is the information transfer index). High k is essentially the effective quantity theory of money for high inflation, whereas low k means the ISLM model is a good effective theory for low inflation (or we just have something more complex as I discuss in the quantity theory link). This means that monetary policy would be more effective in a high inflation environment than in a low inflation environment. I've also discussed "lowflation" regimes before here.

This brings up another topic. On Twitter, Srinivas pointed me to a new SF Fed paper [pdf] on monetary policy effectiveness that comes to similar conclusions based on the data: there are low inflation regimes where monetary policy is less effective than in high inflation regimes.

Actually, as indicated by one of the graphs in my reply, I've been discussing this since the first few months of this blog (almost 4 years ago).

One difference between the inflation (i.e. k) regimes and Bullard's regimes is that there isn't "switching" so much as a continuous drift. You don't go from high k to low k in a short period, but rather continuously past through moderate k values over a few decades.

Is there a way to connect lowflation to dynamic equilibrium? Well, one possibility is that we only have "high k" during shocks but we lack enough macroeconomic data to be able to see this clearly – the shock from the first half of the post-war period has only faded out recently.

However, this would make more sense of the fact that all countries haven't reached low k in the partition function/ensemble/statistical equilibrium picture. It's a question that has floated around in the back of my mind for awhile ‒ ever since I put up this picture (from e.g. here):

The problem is evident in that light green US data as it comes from the Depression. That means the US was once at "low k", but then went to "high k" in the WWII and post-WWII era and has since steadily fallen back to low k. The problem is that while the ensemble approach can handle the drift towards lower k values (i.e. the expected value of k falls in an ensemble of markets as the factors of production increase), the mechanism for increasing k involves ad hoc modeling (e.g. exit/reset through wartime hyperinflation).

However, what if shocks (in the dynamic equilibrium sense) reset k to higher values (in the ensemble sense)? If we take this view, then there might be different growth "regimes", but they split into "normal" and "shock" periods (the red bands in the graphs above). The shock periods can have different dynamics depending on the shocks (e.g. the fluctuating RGDP due to the mis-match between the shock to the price level and the shock to NGDP). Outside of these periods, we have "normal" times characterized by e.g. a constant RGDP growth (the gray line described in the graph above).

Which view is correct?

Given the quality of the description of the data using the dynamic equilibrium model, I don't think Bullard's regimes capture it properly. We have a shock that includes both high and low growth, but the low growth regimes on either side of the shock (today and the 1950s) represent the "normal" dynamic equilibrium (the low RGDP growth period of the 1970s wasn't the dynamic equilibrium, but rather just a result of our measure of the GDP deflator and definition of "real" quantities). This is evident from the good match between the RGDP data and the theoretical curve that is just NGDP/GDPDEF (NGDP divided by the GDP deflator). NGDP and the deflator have one major shock in the 1970s that turns into a fluctuating growth rate simply because the difference of two Gaussians [1] with different widths fluctuates:

The two high growth regimes and the intervening low growth regime are simply due to this. Occam's razor would say that there is really just one shock [2] with different widths for the different observables centered in the late 70s instead of three different manifestations of two growth regimes (per Bullard).


[1] The derivative of the step function in the dynamic equilibrium is approximately a Gaussian function (i.e. a normal distribution PDF), and when you divide NGDP by DEF and look at the log growth rate you end up with the difference of the two Gaussians.

[2] This is the same shock involved in interest rates, inflation, employment-population ratio, etc so we should probably attribute it to a single source instead of more complex models (at least without other information).

Tuesday, April 18, 2017

A tour of information equilibrium

I posted an org chart of information equilibrium concepts yesterday; today I created a presentation that takes you on a tour of the whole thing. It represents a 50-chart summary of most of the work on this blog.

You can download the chart package [pdf] (let me know if my Google Drive settings aren't working for you in comments or via tweet), or you can just look at the images below the fold.

Monday, April 17, 2017

Organization of information equilibrium concepts

The blog's 4th birthday is coming up, so I started writing up a post that'll come out next Monday. However in writing that post I realized that there's a logic to the different techniques I've used that all stem (ultimately) from the basic information equilibrium condition. Here's an organization chart:

Each circle has a post or presentation that sums up the ideas:

Information Equilibrium: This is the circle at the center of it all. An overview of the ideas are in this presentation, this blog post, and my paper (choose your favorite format). The information transfer index k is a key property of an information equilibrium system.

Single-factor production, Supply and Demand: I illustrate both of these circles as well as their connection via scope conditions and scale (time to adjust) in this recent blog post. These scope conditions are shown in the diagram. This is also discussed in the paper.

Multi-factor production: This is behind the Solow model, and is best explained in the paper. This blog post on the so-called "Kaldor facts" is useful as well. It comes from assuming output ("demand") is in information equilibrium with more than one input factor ("supply"). Another example is the "quantity theory of labor and capital" I came up with.

Matching models: In this post, I show how matching models fit into the information equilibrium framework and connect it to dynamic equilibrium (below). The idea is not very different from the two factor approach above where two factors (an unemployed person and a job opening) come together to form an output (a hire).

Dynamic equilibrium: This presentation goes over the main ideas and some results of the dynamic equilibrium approach. It follows from making assumptions about the time dependence of the quantities in information equilibrium (in particular that both are exponentially growing).

Ensembles: This sets up an ensemble of information equilibrium conditions (with one or more input factors of production and information transfer indices k) and uses a maximum entropy distribution (partition function Z) to deal with multiple markets, industries, or firms. It makes rigorous the idea of how the system must behave if there is to be a single "economic growth rate" (i.e GDP growth) that is a well-defined aspect of a macroeconomy. This is also discussed in the paper, though probably not as clearly as the blog post. An explicit example using labor as the single factor of production is shown in this blog post.

Statistical equilibrium, k-states: Going a step further than just looking at ensembles, this looks at behaviors of the distributions of economic "k-states" P(kᵢ) ‒ with information transfer indices kᵢ ‒ and shows how to understand stock markets, government spending, secular stagnation and nominal rigidity. Again, this is also discussed in the paper, but not as clearly as the "mini-seminar" I link to in this paragraph.

Sunday, April 16, 2017

Dynamic equilibrium in occupational classes

David Andolfatto has a post up about trends in employment. One of the things he notes is the "cyclic asymmetry" of the unemployment rate that is pretty well described by the dynamic equilibrium model [1] (also see the underlying matching model). The sequence of shocks leading to lower and lower male participation was also noted in [1]. However, David did put up some data about the fraction of "routine manual" labor that is also well described by the dynamic equilibrium model:

In the second graph, the equilibrium growth rate is (consistent with) zero however I translated and scaled the shocks to show them superimposed on the same graph. Some observations:

  • Routine manual labor shows a similar pattern to male participation rate in [1], however since it is not growing (male participation rate grows between shocks), it just gets hit with shocks and never rises.
  • Female routine manual labor shows roughly the same pattern as male, just from a lower base. The shocks in 2001 and 2008 were a little bigger and a little smaller than the shocks to the male routine manual labor fraction, respectively.

The other occupational classes (non-routine manual, routine cognitive, non-routine cognitive) also display dynamic equilibrium but also show more influence of the non-equilibrium process of women entering the workforce (see also here) that didn't reach equilibrium until the 1990s. A couple of differences:
  • Non-routine cognitive is growing for both men and women (non-zero growth rate, unlike the zero growth rate above).
  • Non-routine manual is growing but at a fairly slow rate for men that was outpaced by women until after the Great Recession.
  • Routine cognitive shows the strongest signal of women entering the workforce in the 80s (e.g. office admin jobs, recalling the cultural touchstones of the time), eventually matching the zero growth equilibrium for men in the 2000s.
Here is what that that last dynamic equilibrium description looks like (you can see that the slope falls until it reaches about the same slope as for men in the 2000s):

Saturday, April 15, 2017

It's a production input. No, it's a market good. Relax, it's both.

From twitter:
Noah Smith‏ @Noahpinion
Why the good ol' Econ 101 supply-and-demand model just doesn't work for the labor market: … 
Dan Davies‏ @dsquareddigest
Isn't simpler - supply and demand models are models for goods, and labour is an input to a production process 
Noah Smith‏ @Noahpinion
That doesn't disqualify it from S-D modeling (oil is also a production input and S-D seems to work OK there, right?). But yeah.
I don't think there could be a more perfect way to bring up the major difference in the information equilibrium model of supply and demand versus the normal understanding. I went into more detail about this in this post, but there is one observation I'd like to make here.

What we have is a model with two "scales". One is the time it takes for demand to adjust to changes in supply. The other is the time it takes for demand supply to adjust to changes in supply demand. Let's call these $t_{d \rightarrow s}$ and $t_{s \rightarrow d}$. We have three major scenarios:

t_{s \rightarrow d} \gg & \; t \gg t_{d \rightarrow s}\\
t_{d \rightarrow s} \gg & \; t \gg t_{s \rightarrow d}\\
& \; t \gg t_{d \rightarrow s}, t_{s \rightarrow d}

In the first, demand moves faster (a shift in the demand curve). In the second, supply moves faster (a shift in the supply curve). In the third, we have adjustment back to "general equilibrium" as both have had a chance to adjust to each other.

According to the information equilibrium condition, we have (for concreteness talking about the labor market with aggregate demand $N$ (possibly from many factors) and labor supply $L$ with abstract price $p$):

p \equiv \frac{\partial N}{\partial L} = \; k \frac{N}{L}

If $N = N(L, x, y, ...)$, then this has general solution:

N(L, x, y, ...) \sim f(x, y, ...) \; L^{k}

but only when we look at time scales in the third regime where supply and demand adjust well before we observe the system. Note that this is precisely the form that operates as a production input for a Cobb-Douglas production function (see e.g. here). In the other two regimes, we treat either $N$ or $L$ as approximately constant, which yields supply and demand curves (per here or here).

So for long times $t \gg t_{N \rightarrow L}, t_{L \rightarrow N}$, we can treat $L$ as a production input. More labor means more output. However, in the case of the labor market, because the labor supply are people who buy stuff we might never have the first two regimes because adding to the labor force also adds aggregate demand.

And this is part of the point I was trying to make in my very long short play. Until you understand the scope of the theory or model under consideration, you're not really "doing science". Instead you are making ad hoc theories like Noah and Dan above. Labor is a production input, not a market good so supply and demand doesn't work. But oil is also a production input, and supply and demand works fine there.

Effectively, without the idea of model scope and scales, you're left with sometimes supply and demand works and sometimes it doesn't which is totally unscientific. Now the information equilibrium picture may not be correct, but it shows at least one way you can understand this idea of "sometimes it works" in a much more scientific and rigorous way.

And that is the more general theme of my short play: (to me) there does not seem to be any real organizing principle for this situation among the hundreds of (macro)economic models. Sometimes you use a DSGE model. Sometimes it doesn't work. Sometimes you use a VAR model. Sometimes it doesn't work. Olivier Blanchard and Dani Rodrik essentially try to make the question a question of methodology. You should use certain models in certain situations or for certain questions. But really it's a question for the models themselves (well, the model's authors). A DSGE model should tell you about its own scope. If it fails to perform within that scope, then it should be rejected.

And this is where the math comes in because it shouldn't be economists just declaring the model's scope by fiat (that's what Blanchard is basically doing in his blog post, but not even about specific models but rather for whole classes of models ‒ to borrow a phrase from the British, it does my head in). You should show how the scope conditions apply due to the mathematical assumptions. In the information equilibrium model above, you can literally only derive the supply and demand curves mathematically by making assumptions about how fast supply and demand change (i.e. setting scope conditions). There are no supply and demand curves if we ignore the scope conditions listed above, only production functions.


PS I am not in any way saying adjustment time is the proper or even only scope condition. This is just one of the simplest ‒ i.e. something that should be taught in Econ 101 as an example, but in graduate school you move on to more complicated models.


Update: There are some simulation animations here of these two regimes. The simulation below shows a case where demand adjusts a bit slower to an increase in supply resulting in a fall in the price:

Over time ($t \gg t_{d \rightarrow s}, t_{s \rightarrow d}$) we return to the production input view where $D \sim S^{k}$ and $P \sim S^{k-1}$.

Update, the second: I should add that there is a fourth regime, but it's trivial:

t_{d \rightarrow s}, t_{s \rightarrow d} \gg t
In this regime, nothing happens.

Friday, April 14, 2017

Is economics scientific? A short play in one act.

[Oikonomios, an academic macroeconomist, runs up to Epistimia, a theoretical physicist, in the hallway at a university. Shouting from a chorus of voices is heard outside.]

Chorus: Economics isn't scientific!

Oikonomios: Epistimia, help! I can't get away from the complaints that economics isn't scientific!

Chorus: Economics isn't scientific!

Oikonomios: See?

Epistimia: Well, they do have a point.

Oikonomios: What?! We respond to evidence; that makes economics a science!

Epistimia: Courts also respond to evidence, but that doesn't make them scientific. That's just being rational.

Oikonomios: We have accumulations of evidence that confirm the applicability of some theories and reject the applicability of others. That should be Popperian enough for an inexact science.

Epistimia: Please don't mansplain science to me. You remember I'm a physicist, right? Science is about much more than positing hypothesis and accepting or rejecting them. That's grade school science class stuff. It's about not fooling yourself. It's about knowing the limitations of your theories and where your assumptions fail. It's about understanding scope. Falsification is a false dichotomy. Popper thought that Einstein's theory of relativity falsified Newtonian gravity, but no physicist would ever think of it as "false". We still teach it ... even in graduate school.

Oikonomios: Sorry. But you do think of general relativity as a better theory, right?

Epistimia: Yes, its scope is much larger than Newtonian gravity, but it isn't consistent with quantum mechanics for example. And it's hard to calculate things with it sometimes. Within its scope, it is a great theory, but then so is Newtonian gravity.

Oikonomios: You mentioned scope twice now ... what do you mean?

Epistimia: Where the theory or model is valid.

Oikonomios: We use data to tell us which models are more applicable.

Epistimia: Ex post or ex ante?

Oikonomios: Ex post ...

Epistimia: [Interrupting] You figure out which model to use ex post?!!!

Oikonomios: [Continuing undeterred]... how could you possibly figure out if a model is applicable before you have any data?

Epistimia: You did build this model, right? It isn't some sort of black box teleported here by aliens or something?

Oikonomios: If you're going to be like that, I think I'd prefer to deal with the chorus ...

Chorus: Economics promotes neoliberalism!

Oikonomios: Maybe not ...

Epistimia: It's just so shocking to me that you'd build a model where you didn't know where it should fail based on the assumptions you made in building it.

Oikonomios: Well that part is really a craft, not a science, especially when the choice of which model has to be made in real time. You could use heuristic decision-making in some cases, but rational choice in others.

Epistimia: But you know which one should work before going in, right?

Oikonomios: Not necessarily ... that's the craft!

Chorus: Economics isn't scientific!

Epistimia: Sure, there's some judgment involved and sometimes you don't know for sure ‒ sometimes you make a discovery. But it shouldn't just be craft. For example, I read all the time about how your rational agent models can't explain individual choices.

Oikonomios: Yes, but rational agents can work fine for some other cases. That's why we sometimes think about behavioral economics.

Epistimia: The scientific thing to say is that rational agents are a possible effective theory when you don't have just one or two agents but rather lots of agents. Physicists treat atoms like tiny hard spheres even though we know that's wrong, but only when we're looking at a large system where there are lots of atoms that are far apart.

Oikonomios: In my class, I once drew a huge tree on the blackboard that showed how most of economics could be derived from principles of rational choice. But go beyond the basics, and add in complications involving information and transactions costs and you very quickly derive competing models.

Chorus: We want one-handed economists!

Oikonomios: I wish they'd be quiet for a minute.

Epistimia: Me too, because I think we're going somewhere here. So you have models that are contradictory when you add different effects, but you should be able to determine that the models either don't have scope in common because they operate at different scales ‒ like general relativity and quantum mechanics ‒ or that one is definitely wrong. When you add transaction costs, there's a certain scale where they don't matter right?

Oikonomios: I have a good story about that. At the end of the first year of graduate school in economics, they make you take long tests on micro- and macroeconomics.

Epistimia: It's the same with physics. Classical mechanics, quantum mechanics, electromagnetism, thermodynamics ...

Oikonomios: Anyway, my micro test lasted five hours, and I still remember a question I missed. It was about those transaction costs: It asked what happened if buyers and sellers had to row from island to island in order to exchange their goods. It turned out that this so-called transaction cost, even though it was tiny, made the market break down ‒ no one bought or sold anything.

Epistimia: Wait, you're saying even a transaction cost that was very small compared to the scale of the transactions qualitatively changed the properties of the system?

Oikonomios: Yep.

Epistimia: Nonperturbative economics, huh? But there are transaction costs in the real world and people buy and sell stuff. What use is this model?

Oikonomios: It's really a toy model. It allows for a quick first pass at some question, or presents the essence of the answer from a more complicated model or class of models. They work as pedagogical devices. They are art as much as science.

Chorus: Economics isn't scientific!

Epistimia: I think I'm back with the chorus on this. How exactly does a toy model where negligible transaction costs stop all economic activity teach anything when it does not describe the real world?

Oikonomios: Sometimes transaction costs are too high and so market activity never gets started.

Epistimia: Yes, but that's not the model you were describing before. That sounds like a model with a scope condition saying transaction costs are small compared to the scale of the goods' value or profits or something. The original sounds like some theory with global scope where any transaction cost greater than zero breaks down the market.

Oikonomios: I'm not sure I understand the difference.

Epistimia: That model in your test question is falsified in Popper's sense. If there are no scales that set the scope, it's like having a building without fire doors. The whole edifice burns down. The fact that there are active markets that have transaction costs burns down the whole islands model. It doesn't burn down a model where transaction costs have a scale.

Now it's true that Newton probably didn't envision his theory of gravity as having a scale where it might fail. Physicists didn't really think that way back then. But now we understand that Newtonian gravity applies when gravitational fields are weak and we can think of the speed of light as fast. Those are its firewalls. The observation of gravity waves doesn't burn down Newtonian gravity. It still applies when it's in scope.

Oikonomios: Does this mean the rational agent model burns down because of the no-trade theorem?

Epistimia: What is that?

Oikonomios: In our rational agent models trading volume is essentially zero. The reason is beautifully set out in Nancy Stokey and Paul Milgrom’s no-trade theorem, which I call the Groucho Marx theorem: don’t belong to any club that will have you as a member. If someone offers to sell you something, he knows something you don’t.

Epistimia: Are you saying there is an economic theorem out there that says no one will trade in the stock market? This is a theorem? What is this, real analysis?

Oikonomios: Actually the paper has three theorems in it. It has deliberately strict assumptions to make a point about information and rational expectations in markets.

Epistimia: Hopefully that point is that information doesn't set the scale of trading volume.

Oikonomios: Actually, it's trying to say that traders don't have rational expectations but instead more limited ... Wait, what?

Epistimia: Well my intuition says that if your agents are just a little bit irrational, then you should just get a little bit of trading volume unless it is highly non-linear. Irrationality sets the scale of trading volume, not information. What happens if you have random agents?

Oikonomios: You mean noise traders?

Epistimia: That sounds kind of derogatory. I'd say their motives are just unknown. Maybe they're selling stock for a loss because they have medical bills to pay.

Oikonomios: Well, we call them noise traders. And Stiglitz and Grossman added them and found that noise traders would mean that volume wouldn't be zero.

Epistimia: So random traders set the scale of the volume in the market?

Oikonomios: I don't think I would put it that way ... 

Epistimia: More random traders means more volume?

Oikonomios: Well ... yes.

Epistimia: Then given rational agents on their own don't trade at all and random traders set the scale for market volume, you're really verging on a model where the information content of trades doesn't play a big role in the market but rather just the number of people who participate. The scale you should look at to determine market volume is the number of people who own stock, not the information content of the trades. Of course the scope of that theory would be that the number of rational agents is much smaller than the total number of agents ...

Oikonomios: Interesting. I have not seen economists spend much time thinking about scope and scale. But it's an important topic to think about. I used to nod off when physicists interested in macro went on about scaling. I should have paid more attention.

Epistimia: And stop using falsified models as pedagogical devices.

Oikonomios: I should suggest we take supply and demand out of the curriculum at the next faculty meeting, then. That's probably a good idea. Sadly, though, I bet that we won't.

Epistimia: Really?! That always seemed to me to be one your field's better ideas. It works for Magic, The Gathering cards.

Oikonomios: Well, not in labor markets. The basic supply and demand model suggests even a modest minimum wage should significantly reduce employment, but economists discovered that the evidence did not show this. As this evidence accumulated, monopsony and search models were thought to be more relevant.

Epistimia: So you use those other models to limit the scope of the supply and demand diagram?

Chorus: Economics isn't scientific!

Oikonomios: Well, as you said ... there are no scales in a supply and demand diagram. A single problem burns the whole model down.

Epistimia: But, but ... Magic cards?

Oikonomios: A lot of right wing people use wrong-headed supply and demand arguments to promote policies they want. Like saying a minimum wage costs jobs or immigration lower wages.

Chorus: Economics isn't scientific!

Epistimia: The latter always sounded like a scope problem to me.

Oikonomios: How so?

Epistimia: Well it seems unlikely that adding thousands of people to a city could increase the labor supply without changing the demand.

Oikonomios: Yes, we say that general equilibrium is important in that case. Supply and demand diagrams are partial equilibrium.

Epistimia: That's a scope condition! The supply and demand diagram always moves demand or supply. If both move, you can get anything you want. That's basically an assumption about supply moving faster or changing a lot compared to how fast or how much demand changes. In the case of immigration, you can't increase supply without increasing demand. You can however easily print up a million Magic cards much faster than the nerd demand changes, so supply and demand is in scope there.

Oikonomios: The chorus probably won't be happy with you defending neoclassical economics.

Epistimia: I think they've moved on ...

Chorus: Economics can't forecast!

Oikonomios: Ha! Silly people! Economic models can't predict the future! Think of economists like doctors. We can provide advice on the best course of action when illness strikes. However, we would never dream of condemning doctors because they cannot predict the exact time of our death, still less suggest that this failure indicates they are not doing science.

Epistimia: I'm back with the chorus on this one.

Oikonomios: What?! Physicists can't predict earthquakes, so maybe you're not doing science then.

Epistimia: We have some pretty good theories about nonlinear mechanical failure mechanisms with several different applications that imply that it's really hard to observe the initial crack that leads to a failure in the fault line making them a bit random. However geophysicists can predict where earthquakes are likely to occur. Those doctors can't predict when you'll die of heart attack due to a tiny blood clot, but they know some risk factors. And they do have an idea of how many heart attacks there will be when looking at a large number of people. But really, what is the state of knowledge here? Does economics know that recessions are cascading failures that are triggered by some tiny event?

Oikonomios: There are some network models where that happens. And there are information cascades and the failure for expectations to be consistent ...

Epistimia: But we just said information doesn't set the scale for ... ah, forget it. Sure, if you assume recessions are random events, then you can't predict them. I'm not sure you've made a good case that economists really know what recessions are other than a collection of plausibility arguments. But even if it's true that recessions are random processes, why can't you forecast in the absence of recessions?

Oikonomios: The chorus is talking about the Great Recession.

Chorus: We love Steve Keen's overly complicated models that aren't empirically accurate either!

Oikonomios: Actually I'm not sure what they're talking about.

Epistimia: Neither do I. Keen seems to think economies are like complicated nonlinear electronic oscillator circuits, but you'd never figure out the circuit elements from less than 100 years of macroeconomic data and only a few business cycles. But let's not get distracted ... I'm talking about the failure of DSGE models to forecast even when there's no recession.

Oikonomios: You're just using DSGE as a four-letter word.  It is worrying to see the practice of rigorously stating logic in precise mathematical terms described as a flaw instead of a virtue.

Chorus: DSGE stands for Doofuses Study Garbage Economics!

Epistimia: Yeah, um, don't forget I'm a physicist so I'm totally cool with math. And I agree that stating things mathematically is definitely a big step towards testing them. But those "precise and logical" [Epistimia makes air quotes with her hands] DSGE models fail to forecast even a few quarters ahead; they do worse than an AR process.

Oikonomios: They have their issues.

Epistimia: The have 50 parameters!

Oikonomios: That's one of their issues.

Epistimia: You just took a model that says unemployed people are actually on vacation and added that prices don't change very fast!

Oikonomios: I agree that seems too much at odds with reality to be the best starting point. But their purpose is not to forecast. Their purpose is to explore the macro implications of distortions.

Epistimia: ...

Oikonomios: Fitting reality closely should be left to policy models.

Epistimia: ...

Oikonomios: Policy models are for designing ... Why are you just staring at me with your mouth open?

Epistimia: I'm not sure, but I think my brain exploded because the science in my head just came into contact with anti-science.

Oikonomios: Hey, research is hard!

Epistimia: Research is hard, but this isn't. How can you believe a model when it moves to a different location in parameter space ‒ distortions ‒ when it does so terribly when it moves to a different location temporally ‒ forecasting?

Oikonomios: Well,  path dependence for one ...

Epistimia: But DSGE models contain only a finite number of lags and the infinite future is cut-off by a discounting factor. They exist in a finite temporal universe. Move forward in time past the discounting time scale or backward before the last lag and that piece of the 50 dimensional parameter-temporal space is independent of the original. There can't be any path dependence except on the scale of the theory. Therefore a model in a different piece of parameter space is not any different than a model in a different piece of temporal space in any way that would make you think that not being able to forecast is bad, but you can still look at distortions.

Oikonomios: Actually, Woodford showed how expectations in the infinite future can have an impact on the present.

Epistimia: Long time horizons compared to what scale?

Oikonomios: What do you mean? He looks at the limit as time goes to infinity.

Epistimia: You can't just take a limit as time goes to infinity.

Oikonomios: Mike Woodford is like our Ed Witten, he probably doesn't make major conceptual errors. I don't see why you can't take a limit as time goes to infinity.

Epistimia: Because time has units. Seconds, years, whatever. Infinity has no units.

Oikonomios: So?

Epistimia: So you need to compare the time to something else with the units of time to make a dimensionless parameter you can take to infinity. Like that discount rate. You can look at times further out than the discounting horizon and write ... where's a chalkboard ...

[Epistimia starts looking around.]

Oikonomios: I guess you could compare it to the rate of belief revisions ...

[Epistimia stops looking around.]

Epistimia: That's a start. So time is long compared to the time it takes to make a belief revision.

Oikonomios: Which, if I recall correctly, is then sent to zero.

Epistimia: ...

Oikonomios: What?

Epistimia: My brain just exploded again.

Oikonomios: That's perfectly rigorous math.

Epistimia: It's totally fine in high school calculus to take a double limit with two variables that don't represent anything. It wasn't the math ‒ it was the fact that we live in a real universe and those variables represent real things.

Oikonomios: What now?

Epistimia: Zero also doesn't have units, so we can't compare time to the scale of the inverse rate of belief revisions while sending the rate to infinity. There are not four limits where you take one to infinity, the other to infinity, or both to infinity in different orders. There are only two limits that make sense. One: [Epistimia holds up one finger] Revision time is long compared to the time horizon such that you don't revise before you reach the horizon. Two: [Epistimia holds up two fingers] Revision time is short compared to the time horizon, so you revise well before you reach the time horizon.

Oikonomios: There are so four limits! Paul Romer used basically the same limit in his mathiness paper taking the limit as time goes to infinity and the rate of knowledge growth, called beta, goes to zero in different orders to show that the limit did not converge uniformly.

Epistimia: This is sounding more like real analysis than economics again. Uniform convergence. Ha! Is there an economic theorem that says the inflation rate is transcendental? Do you worry about compactness?

Oikonomios: He proved a mathematical proposition about it. There are definitely four limits. T goes to infinity, beta goes to zero, beta then T go to zero and infinity, and T then beta go to infinity and zero. The last two are different so you don't have uniform convergence.

Epistimia: There are two limits! Beta times T is big or beta times T is small! Are you saying proving theorems is doing economics?

Oikonomios: Economic models, and the math involved, are ways of organizing your thinking.

Epistimia: Sounds like your thinking might be pretty cluttered if you need so many models to organize it for so many different situations ...

Oikonomios: We write down mathematical models. That makes us scientific. Our papers look just like physics papers with all those neat LaTeX symbols ...

Epistimia: Math alone isn't really science! You don't collect data and compare the Banach-Tarski paradox to the real world in order to reject the axiom of choice. Where is that chorus?

Chorus: Economics isn't scientific! Economics isn't scientific!

Oikonomios: There are four limits!

Epistimia: There are two limits!

[Epistimia starts running down the hallway towards the shouting chorus.]

Epistimia: Economics isn't scientific!

Chorus: Economics isn't scientific!

*  *  *

This dialogue/short play is based primarily on Simon Wren-Lewis's recent blog post about economics as an inexact science:

There are several cases above where I copied and pasted from his post with some editing to make it work in a dialogue. However it is also supplemented by a variety of other sources including Ricardo Reis's recent paper, some articles and blog posts from Noah Smith [BloombergView, Noahpinion], Olivier Blanchard's recent blog post [PIIE], a tweet from Paul Romer, an article from Dani Rodrik [Project Syndicate], a blog post from John Cochrane, and a presentation from Michael Woodford. These are listed below:

... and there are a couple references from my blog:

The bit about limits ...
The bit about Magic cards ...
The bit about financial market volume ...

PS I referred to it above pretty consistently as "model scope" or "scope conditions", mostly because Noah Smith called it that and he's a much more widely read blogger than I am so his terminology is more likely to stick. However, in his post he says:
I have not seen economists spend much time thinking about domains of applicability (what physicists usually call "scope conditions"). But it's an important topic to think about.
I'm a physicist, but I do not believe I have ever heard them called scope conditions ("domain of validity" or "scale of the theory", yes, but not "scope conditions"). Maybe it was some other sub-field besides particle physics, or possibly a particular teacher Noah had as an undergraduate physics major. My quick research on the internet makes me think that it's more of a sociology term.

PPS That last bit is a reference to this via this.