Friday, January 29, 2016

False dichotomy (as in: both choices are false)

John Cochrane gives us a false dichotomy on slower growth:
I still suspect that slow growth is resulting from government-induced sclerosis rather than an absence of good ideas in a smoothly functioning economy.
Those really aren't the only two choices, and in fact those effects seem to be based on small effects rather than large ones. In a sense, it is like saying the energy levels of Hydrogen are mostly due to the Lamb shift rather than Coulomb's law. Let me explain. First, technology.

There are major inventions that have completely changed our lives, yet don't seem to have impacted economic growth. For example, there is the famous saying that computers (or the internet) show up everywhere except productivity. My job is entirely different from what it would have been 20 years ago. Even in the past 10 years, I've gone from needing supercomputers to doing the same work with a laptop (with the right GPU). But Robert Gordon (whom Cochrane is objecting to) doesn't think computers are important. From Krugman's review of Gordon's book:
Developments in information and communication technology, [Gordon] has insisted, just don’t measure up to past achievements. Specifically, he has argued that the I.T. revolution is less important than any one of the five Great Inventions that powered economic growth from 1870 to 1970: electricity, urban sanitation, chemicals and pharmaceuticals, the internal combustion engine and modern communication.
Gordon seems to have post hoc definitions of when inventions are great -- the ones that came before periods of high growth -- that renders the technology explanation circular. If computers and networking aren't the kind of inventions that lead to major growth, then there is something seriously wrong with the theory. 

And how these inventions lead to growth depends critically on your theory of growth. Sure productivity could be enhanced by urban sanitation (increased real output per person because people are sick less often). But urban sanitation would be critically important in my quantity theory of labor [1] where urban sanitation leads to simply more people (fewer dying). Electricity doesn't actually increase the quantity of labor like sanitation does in the QTL, but rather adds hours in the evening for some kinds of work -- likely a second order effect. 

In contrast, urban sanitation would have no direct effect in the monetary information equilibrium model where slow growth seems to arise as an entropic force (see here or the paper [2]). A large economy simply has more ways that it can be realized in terms of many slowly growth markets than a few high growth markets making the former simply the more likely state -- regardless of what products or technology exist in the economy.

Now, what about government?

The US federal government increased its size (measured in money) relative to the economy (measured in money) gradually from about the 1930s to about the 1970s (with the exception of WWII). Any person with even a modicum of math skills would see that:

NGDP(G) = NGDP(0) + c₁ (G/NGDP(0)) + c₂ (G/NGDP(0))² + ...

With G/NGDP ~ 0.2 and natural coefficients, that means it could be at most a 25% effect, not an order 1 effect. And it started as a 5% effect prior to the 1930s. Ok, so we have a scale for the effect of government as a fraction of the economy. What now?

Well, as Gordon mentions the 1970s were the end of the period of rapid growth -- meaning that growth slowed when the scale of government impact on the economy stopped growing. And since then, growth has gradually declined even when the government remained about the same size relative to the economy. So at the aggregate macro (dimensionally reduced) level, there is no obvious direct effect.

Yes, this is a back of the envelope calculation. But it means any negative impact from government would have to be unnatural (the c's are large or small or both), highly nonlinear, and/or depend critically on a serious lack of dimensional reduction in aggregating agent behavior. True to form, Cochrane does think there is a serious lack of dimensional reduction (he suggests various microeconomic policies that he thinks integrate into a macroeconomic effect). So at least he is consistent. 

But no one has ever shown this happens. No agent model has ever been aggregated and produced empirically accurate results that depended on agent micro parameters. As I've said before, if dimensional reduction doesn't occur, then economics is probably computationally intractable. And I think there is strong evidence that dimensional reduction does occur -- if only because the models [1] and [2] do pretty well with huge amounts of dimensional reduction.

Speaking of [1] and [2], neither have first order impacts from the government, and second order (at the aggregated macro scale) impacts (from immigration and equal rights/gender equality in [1] and the size of the government and/or financial sector in [2]).

So neither government nor technology seem like the the most plausible mechanisms to describe the steady decline in US growth. At least not without proposing very tedious and complex models that have no hope of being empirically rejected ... because macro data is uninformative for such tedious and complex models.



Additional thoughts on this subject from Noah Smith. And he really gets at a good point. If we want to know how much technology has improved our lives (or government bureaucracy has made things annoying or difficult in business or our personal lives), then we should look at that subjectively. You can tell histories, but leave out the math.

I said before (paraphrasing): the greatest trick economists ever pulled was that NGDP is about our well-being. It's not. Money is an allocation algorithm, full stop and we could reach the current US NGDP without ever developing any technology.

Update, the second (30 Jan 2016)

Dietrich Vollrath as a good blog post up about the persistence of technology. Basically, all of the inventions you had at one time (1500 AD, in this case) is fairly predictive of future growth. The identity of the inventions don't matter for this prediction. But think about what else that means: all of the inventions between the 1500s and the 2000s don't matter to the prediction either. As Vollrath puts it:
In that sense, it isn't the technology in 1500AD per se that matters in the CEG regressions, this is an indicator of some kind of variation in culture or institutions (or something else?) that matters. To return to the earlier discussion, it seems likely that their results won't ultimately turn out to be causal, but the predictive power is telling us to something about how powerful those cultural/institutional [Ed.: or something else?] factors are.
I added the second something else (Vollrath included it in the first sentence, so felt it was appropriate). Maybe more inventions is a sign of a higher entropy economy? More dither?

I also changed the sentence above from "First, growth." to "First, technology." because that is what I meant.


  1. Jason, what do the large blue square and the large gray square in your figure represent? I have a feeling they're related to government and technology. Is their position important?

    Also, I found a mention of "natural coefficients" here. Is that related to your use?

    1. I'm going to claim sub-modicum math skills in my defense.

    2. Government/financial sector per the link in the post.

    3. And "natural coefficients" means roughly o(1). A dimensionless coefficient of a thousand is unnatural, so is a dimensionless coefficient of a thousandth.

      In physics you'd get things like pi/2 out front, but never 1000 pi (unless something weird was going on). This is the reason that the axion was proposed -- a coefficient in the QCD lagrangian wasn't natural (it is less than a trillionth).

  2. Economists- using math to reinforce unconscious moral biases since 1776...

  3. I used this post as a basis for a question to John, which he answered right away. It sounds like he's saying there was a "trichotomy" but it was reduced (by Gordon's book) to the dichotomy he presented.

    I was tempted to follow up with a link to a plot of your CLF based NGDP model, and perhaps one other (like your Solow-like model) and ask "Surely there are other alternatives. For example here are plots from a couple of simple power law models...." But I'm not sure how you feel about that.

    I saw in the news yesterday a headline that went something like this:

    "People like the description of this immigration policy... until they find out it's Obama's"

    I'm often curious to see how someone like John responds to your models, but I've never seen him respond to one of your comments. This leads me to sometimes post a link to one of your plots (on it's own) before explaining the source. My intention is to get the person's reaction before they dismiss it out of hand from an a priori anti-Jason-Smith bias. I don't know that such a bias exists, but sometimes I wonder. Of course, should there be any follow up comment I would reveal the source. But if you'd prefer I not do that kind of thing, I won't.

    1. I don't think I usually ask direct questions. On a higher traffic blog like Cochrane's, he'd probably do what I do sometimes with comments that are just comments (that don't misunderstand something I said): just let them stand.

      At best, real economists (with phds in it) would see some physicist offering up ideas for macro much like how an engineer might look at a sociologist offering up ideas about systems engineering ... with a low prior probability of it being useful.

      I think Tyler Cowen had probably the most open reaction (although this was to a high-status famous physicist):

      I didn’t “get” where [Lee Smolin's] paper is headed (OK, you put in gauge invariance but comparative statics are still hard to predict a priori), but I’m always interested to see how top minds approach the foibles of the economic method.

      But then we come to the real world of the internet. As a physicist, I got a few emails a week about how quantum mechanics or relativity was wrong and I didn't even have a blog with a comment section. I imagine as a prominent economist, you'd get a lot of theories suggested to you ... probably > 95% of which are either already part of the literature or useless (or both). Using that number, any particular comment that says "hey look at my explanation of this effect" gets assigned a < 5% prior probability.

      The truth is I knew this would be a hard slog -- it'd be a hard slog even if I were a professor of economics (e.g. Steve Keen). The only kinds of people who are usually allowed to suggest new approaches like this one are the Lucases, Krugmans and Famas of the field.

      Anyway, I don't think there is a personal anti-Jason Smith bias, but rather just a general skepticism for anyone suggesting new ways of doing things. Heck, even the mainstream approach has failed empirically for the most part!

    2. Thanks for your thoughts on this. Yes, I doubt they have a personal anti-Jason Smith bias, but I wonder if presented with a simple plot in isolation, with a one line description of what it represents, if that might sometimes be more inviting for an econ PhD to consider. They might think "Hmm, that's interesting, I wonder if there's any sensible reason that relation holds." Whereas if they see the information equilibrium theory up front, they might think "WTF?" or, if they've seen it before "Oh, THIS guy [eye roll]." Or maybe they've noticed the same thing presented in the plot themselves and already have or know of an explanation, which would be interesting.

      I suggested an example alternative explanation in words (low CLF growth) to John, but I didn't hear back.

      Prior to John's post, I did use your CPI-CLF plot of Japan with Sumner. I gave a very brief explanation, and asked if he expects a gap to open between the curves. He asked what CLF was, so I explained, and today he responded:

      "Tom, I don’t like the term ‘model’ in that graph, it could cover a multitude of sins."

      Oh well. I gave him a link to your post (where the sins are to be found, if any) and left it at that.

      Meanwhile I notice John Handley and Scott have continued with their long comment exchange. I asked John the other day if he shares your view that MM is unfalsifiable, and he confirmed that's the case.

    3. Also I gave Beckworth a link to the post & plots. His reaction was that it shows correlation but probably not causation. At least he didn't say "spurious correlation."

      This recent negative IOR policy by Japan and it's effects on the market seemed to have Sumner expecting the "finance approach" pundits (e.g. Izabella Kaminska) to be admitting that they were wrong about negative IOR being contractionary. Within 5 minutes (I asked). That is if they were reasonable I suppose.

      So I proposed that if 5 minutes was all that was required for even those with a strong disconfirmation bias to see the efficacy of negative IOR, then the Japanese will surely have noticed, and we shouldn't hear any more about Japan struggling to meet any targets a year from now. I didn't get buy in on that though.

      I think back to your post in which you concluded that MM appears to be a system of thought designed solely to attack any basis for fiscal policy.

    4. Good points all. May be a bit wishful thinking, but I hope that as Fielitz and Borchardt's approaches get more publicity, and prove themselves to be useful in more systems, that the information transfer approach to science will be more generally accepted. Jason is just about 10 years ahead of his time.

    5. Todd, I found what appeared to be an abstract for the EEG paper you did with Jason, but I didn't find more. Can you give any details? Was it published? Is it behind a paywall?

    6. Five minutes is too short for macro data to even come in, so I imagine Sumner was thinking of the market reaction (which may well be wrong as I've noted before several times).



      (1) P = a log L + b

      as "a model" anywhere outside of statistics class isn't really appropriate (in which case any equation that doesn't come from statistics is called a model). The best way to present the information equilibrium model would be as:

      P ≡ dN/dL = k (N/L)

      or as its solutions

      N ~ k log L
      P ~ (k - 1) log L

      which captures the logic behind the equation (1). But in general really needs the information theory behind it to be considered "a model". The information entropy of the states behind the time series N is equal to the information entropy behind the states in the time series L, and P changes in response to signals from N being received by L (or vice versa).

      It is kind of like presenting

      (2) E = (1/2)α²m/n²

      as a model. The model is the Schrodinger equation/quantum mechanics, (2) is just a result for the energy levels of Hydrogen.

    7. Tom, the paper hasn't been published yet. That was an abstract for a poster session.

    8. ...and yes, he was thinking market reaction, and I recall you noting it could be wrong.

    9. Tom:

      Also, I would choose the rate graphs, not the level ones as exemplars. Everything in economics is some kind of growth curve.

    10. And thus level plots are too easily written off as potentially spurious correlations?

    11. More like there are tons of other time series you could put in the model instead (so it isn't unique). The level of employment should roughly correspond to the level of output (so it isn't spurious -- there is probably something happening there).

  4. This is an interesting post but it reflects a key problem with economists. They tend to talk about concepts in the abstract rather than using examples. By generalising the concept, they lose all sight of what is interesting. Capital, productivity and technology are amongst the victims of this concept abuse.

    Imagine that a chef claimed to be an expert in ‘recipe’. No-one would take him seriously. The concept of ‘recipe’ is not particularly interesting. It is knowledge of individual recipes, and the nuances of taste created by different ingredients and cooking methods, which are interesting.

    Similarly, we can learn a lot in economics, and we can ask a lot of interesting economic questions, by thinking about examples of concepts rather than the concepts themselves.

    I often buy my groceries by ordering them online and having them delivered. This is only possible because of technology. The benefit to me is an increase in quality time. A rough calculation shows that we get about 50 hours of quality time each week after sleep, hygiene, work, shopping, chores etc. If I can save 90 minutes of my non-quality time by ordering my groceries online and avoiding a trip to the supermarket, I have increased my quality time by 3%. That is an important benefit to me but it is entirely invisible to economists who think only in terms of GDP, so they conclude that technology is not very important.

    More generally, food is an example of a post-growth market in advanced western societies. We now have more than enough food to eat. If people go hungry, it is a distribution problem rather than a capacity / lack of growth problem. As a result, supermarkets now complete by improving product quality, providing added-value services and using personalised pricing and marketing. All of these things are invisible to the economists who live in the GDP swamp.

    The technical problem here is that it is difficult to measure economic benefits as they are often intangible and, even when they can be expressed as tangibles, such as in my 3% quality time improvement, we do not have any mechanisms to capture these measurements.

    Jason often says that macro data is uninformative. I agree. There is no way that economists could figure out that people like me are trying to optimise their quality time, or supermarkets are competing on product quality, if the only concepts in their mental models are traditional measures such as GDP, money supply, inflation and exchange rates. That suggests to me that there is a serious mismatch between interesting economic questions and current macroeconomic techniques.

    1. Jamie, I think you hit on something that gets at the heart of what my blog has been about:

      That suggests to me that there is a serious mismatch between interesting economic questions and current macroeconomic techniques.

      Indulge me in a paraphrase:

      That suggests to me that there is a serious mismatch between interesting scientific questions (species adaptation, life in the universe) and current physics techniques.

      At one time, some physicists did have some contributions to biology (e.g. Schrodinger's What is Life?), but really since the beginning physics techniques were never matched up with scientific questions from biology. Hence they are different fields.

      In my view, the subjective impact of technology on our lives is the domain of sociology anthropology, and history. It's economic impact can vary from nil to huge.

      Another analogy: in some cases, the biosphere has limited impact on our understanding of geology (volcanism, plate tectonics); in others it is huge (carbon and water cycles, oxygenated atmosphere). But in general, you shouldn't start to try to answer a geological question with biology. Start with plate tectonics, glaciation and sea level changes.

      And you shouldn't start with subjective human behaviors, morality, or values to try to answer a quantitative macroeconomic question.

      This is not to deny these have impacts, but rather that the tools of macro and the tools of sociology are mismatched. And the reason is probably that they have little to do with each other and should be separate fields.

      "Technology" in macro bears little resemblance to technology in the real world. That probably means "technology" either is a flawed model (empirically wrong) or is really about something else (I think the thing called "technology" is really a measure of macro entropy).

      Inflation and growth may be nothing more than measures of the size of the labor supply. Sure, there are recessions -- and that may be the interaction of sociology and psychology with macroeconomics. But even the worst recessions (or bubbles) are 10-20% effects. That leaves 80-90% that could just be about numbers of widgets -- and really should be thought of as just that until an empirically accurate explanation comes along.

    2. Thanks for the reply. I see that you have written another post on this subject. I will reply to that later. In the meantime, I will add a further comment to this post on the subject of productivity which is another topic which doesn't fit well in macroeconomics for similar reasons.

  5. "there is the famous saying that computers (or the internet) show up everywhere except productivity."

    Really? My TRS-80 certainly increased my productivity. I had expected it to save me time. Instead, I got more done. It is hard for me to imagine that computers did not in general allow people to get more done in the same amount of time. People are not stupid.

    1. I turned my TI-99/4a into human capital (by learning to program on it). But computers becoming commonplace in the workplace is associated with a period of lower productivity growth.

      I imagine that is because economists' "productivity" (more real output per unit of labor input) doesn't actually measure what we would think of as productivity (increased valuable 'stuff' done per unit time).

      I think TFP measures entropy, but then that's just one possible theory ...

    2. Well, TFP is a residual. Calling it this or that does not explain it.

    3. As for computers becoming commonplace in the workplace, by the time that happens you may be at the point of negative returns. ;)

    4. Just to clarify, the "productivity" you are referring to is actually "Labor Productivity" or Output per worker. TFP is usually a residual but there is also Real Output per Hour which essentially captures "increased valuable stuff done per unit time".

    5. You are right -- I was mostly referring to labor productivity above (I should have put labor productivity), but then referenced TFP as an aside because I had put together a model for that ... but in that case TFP was for labor and capital (i.e. all factors, at least all factors in the model).

  6. The Vollrath paper is interesting. Thanks. :) (But the title is a bit misleading.) But 1500 is the beginning of the modern era. Isn't there a disconnect if we go back to the year, 1,000? At that time the Arabic world was more technologically advanced than Europe, but its advantage had disappeared by 1500. And wasn't China also more technologically advanced than Europe at that time? Conditions in 1500 may be predictive of conditions in 2000, but conditions in 1000 do not seem to be predictive of conditions in 1500.

    1. As Vollrath says, it only explains about 50% of the variation.

      But I think the "dark ages" term has taken a toll on the perception of Europe. The "Carolingian Renaissance" happens around 800 and there was this guy:

      But I don't want to defend the technology view too much. My view is something like this:

  7. Macroeconomic “productivity” is another badly defined concept which I suspect adds little insight.

    I spent many years helping businesses and government departments increase their productivity levels so I know a lot about productivity at a microeconomic level. However, productivity at a macroeconomic level is not the same thing. I don’t think that economists understand this. However, they don’t explain what they mean by macroeconomic productivity, or why it is useful, so who knows?

    A few points using Eli’s terminology. Eli mentions three things.

    The first is TFP which seems to be a residual in a mathematical equation. I don’t understand why that is useful as it doesn’t seem to correspond to anything in the real world.

    The second is labour productivity which is output per worker. That makes sense at a micro level but not at a macro level. Output is heterogeneous so you can’t add it up across industries. Also, in a service-oriented economy, output is often nebulous. For example, what is the output of a lawyer or a mathematical physicist or an economist?

    The third is real output per hour in monetary terms “which essentially captures ‘increased valuable stuff done per unit time’". At least that is something real and it can be added up so maybe it’s useful at a macro level. However, it just begs more questions.

    Let’s return to our lawyer. The monetary output per hour of a lawyer is basically his fee rate so we can improve his “productivity” by raising his fee rate without necessarily making him any more productive at a micro level. Alternatively, if we make him more productive at a micro level by, say, providing him with electronic access to historical casework, but this does not translate into an increased fee rate, there will be no change to macroeconomic “productivity”. Also, we can improve his macroeconomic “productivity” if he can handle two cases at once, rather than one, as he would have two lots of fees, but what if that leads to him losing the two cases rather than winning the original one? Is that a good thing? I suspect not.

    What about the public sector? What is output per hour in the public sector. As the public sector doesn’t sell its services, that can only be based on costs, so that suggests that we can improve the “productivity” of the public sector by raising its costs! That is the opposite of microeconomic productivity.

    Macroeconomic productivity MIGHT be a useful concept if the economy was made up entirely of manufacturing businesses, so maybe the concept was created when the economy had a different composition. However, even there, it seems that there is probably a fallacy of composition.

    Imagine a manufacturing business which produces 500 units of output with 100 employees. Microeconomic productivity is 5 units per worker. Now suppose that the business implements a technology which doubles productivity. That allows the business to create 500 units with 50 workers. Microeconomic productivity is now 10 units per worker. However, that means that the business can fire the other 50 workers whose productivity falls to zero. Macroeconomic productivity does not change as the total economy still produces 500 units and still has 100 workers. Macroeconomic productivity will only increase as and when the fired workers find other jobs. If that doesn’t happen, the microeconomic productivity improvement may not translate into a macroeconomic one.

    Productivity improvement is a vitally important subject at the micro level but I don’t see that it contributes much to a macro level understanding of the economy other than confusion. I can see that it would be useful to compare like with like but that is all e.g. one manufacturing business with another, or equivalent manufacturing in one country versus another country. However, that is comparing microeconomic productivity.

    1. Hi Jamie,

      You said:

      "Macroeconomic “productivity” is another badly defined concept which I suspect adds little insight.

      However, productivity at a macroeconomic level is not the same thing [as microeconomic productivity]."

      I agree!

      You said:

      "The first is TFP which seems to be a residual in a mathematical equation. I don’t understand why that is useful as it doesn’t seem to correspond to anything in the real world."

      Sometimes naming a thing helps insight, sometimes it doesn't. I think this is a case where "real" quantities (adjusted for inflation) and constant returns to scale are the issue -- there is no changing TFP factor in terms of nominal quantities where returns to scale are unconstrained:

      So writing the Solow production function with constant returns to scale and in terms of real quantities forces you to accept a "residual" called TFP.

      I think the root of the problem is defining everything in terms of money in macro ... if we just counted output in terms of widgets and labor hours, there'd be no TFP. But counting output in terms of money (and inflation-adjusted as well) leads to problematic factors.


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